# Florian Luca

#15,972

Most Influential Person Now

Romanian mathematician

## Florian Luca's AcademicInfluence.com Rankings

Florian Lucamathematics Degrees

Mathematics

#946

World Rank

#1647

Historical Rank

Number Theory

#65

World Rank

#95

Historical Rank

Measure Theory

#1342

World Rank

#1689

Historical Rank

## Download Badge

Mathematics

## Florian Luca's Degrees

- PhD Mathematics University of Bucharest

## Why Is Florian Luca Influential?

(Suggest an Edit or Addition)According to Wikipedia, Florian Luca is a Romanian mathematician who specializes in number theory with emphasis on Diophantine equations, linear recurrences and the distribution of values of arithmetic functions. He has made notable contributions to the proof that irrational automatic numbers are transcendental and the proof of a conjecture of Erdős on the intersection of the Euler Totient function and the sum of divisors function.

## Florian Luca's Published Works

### Published Works

- On the equation x2+2a⋅3b=yn (2002) (156)
- On a conjecture about repdigits in k-generalized Fibonacci sequences (2013) (102)
- Analytic Number Theory: Exploring the Anatomy of Integers (2012) (99)
- Fibonacci and Lucas numbers with only one distinct digit. (2000) (94)
- Linear combinations of factorials and $$S$$S-units in a binary recurrence sequence (2014) (80)
- 17 lectures on Fermat numbers : from number theory to geometry (2001) (80)
- Powers of Two in Generalized Fibonacci Sequences (2012) (75)
- Powers of two as sums of two k-Fibonacci numbers (2014) (61)
- Generalized balancing numbers (2009) (59)
- Fibonacci numbers at most one away from a perfect power (2008) (52)
- A generalization of a classical zero-sum problem (2007) (44)
- An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers (2011) (41)
- 17 Lectures on Fermat Numbers (2001) (38)
- On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions ϕ and σ (2002) (37)
- Coincidences in generalized Fibonacci sequences (2013) (37)
- Pell and Pell-Lucas numbers with only one distinct digit (2015) (36)
- On The diophantine equation Fn+Fm=2a (2016) (36)
- Character sums and congruences with n (2004) (35)
- Irreducible radical extensions and Euler-function chains (2007) (35)
- Fibonacci numbers which are concatenations of two repdigits (2019) (33)
- Heron Triangles with Two Fixed Sides (2006) (32)
- Repdigits as sums of three Fibonacci numbers (2012) (31)
- Perfect fibonacci and lucas numbers (2000) (31)
- On the $X$-coordinates of Pell equations which are Tribonacci numbers (2016) (31)
- Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers (2013) (30)
- MOV attack in various subgroups on elliptic curves (2004) (30)
- Rational products of singular moduli (2014) (29)
- Distinct digits in base b expansions of linear recurrence sequences (2000) (29)
- Values of the Euler Φ-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields (2011) (29)
- Powers of Two as Sums of Two Lucas Numbers (2014) (28)
- DIOPHANTINE TRIPLES WITH VALUES IN BINARY RECURRENCES (2008) (28)
- On perfect powers that are sums of two Fibonacci numbers (2017) (28)
- Prime Chains and Pratt Trees (2009) (27)
- On the largest prime factor of (ab+1)(ac+1)(bc+1) (2003) (27)
- Composite Integers n for Which ϕ(n)|n – 1 (2007) (26)
- On a problem of Pillai with Fibonacci numbers and powers of 2 (2017) (26)
- Elliptic Curves with Low Embedding Degree (2006) (26)
- ON THE EQUATION x 2 + 2 a · 3 b = y n (2002) (26)
- On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2 (2017) (25)
- Fibonacci Diophantine triples (2008) (25)
- Fibonacci Numbers with the Lehmer Property (2007) (25)
- An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers (2014) (25)
- On numbers n dividing the nth term of a linear recurrence (2010) (25)
- Diophantine equations with products of consecutive terms in Lucas sequences (2005) (24)
- Almost powers in the Lucas sequence (2008) (24)
- Fibonacci Numbers of the Form k2+k+2 (1999) (23)
- On the exponent of the group of points on elliptic curves in extension fields (2005) (22)
- Common values of the arithmetic functions ϕ and σ (2009) (22)
- Non-Holonomicity of Sequences Defined via Elementary Functions (2006) (22)
- On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers (2002) (22)
- On X-coordinates of Pell equations which are repdigits (2016) (21)
- Sums of Factorials in Binary Recurrence Sequences (2002) (21)
- The Diophantine equation P(x) = n! and a result of M. Overholt (2002) (20)
- The maximum of the degree of nonholonomy for the car with n trailers (1994) (20)
- Fibonacci numbers of the form p a ± p b (2009) (20)
- Functional graphs of polynomials over finite fields (2013) (20)
- Average order in cyclic groups (2004) (20)
- Exponential sums and congruences with factorials (2004) (20)
- Perfect powers from products of terms in Lucas sequences (2007) (20)
- ON THE LARGEST PRIME FACTOR OF THE k-FIBONACCI NUMBERS (2012) (20)
- The Distribution of Self-Fibonacci Divisors (2014) (20)
- Products of Factorials in Binary Recurrence Sequences (1999) (20)
- Quotients of Fibonacci Numbers (2016) (20)
- On factorials which are products of factorials (2007) (19)
- On factorials expressible as sums of at most three Fibonacci numbers (2010) (19)
- Every positive integer is a sum of three palindromes (2016) (19)
- On shifted primes with large prime factors and their products (2013) (19)
- Anatomy of Integers (2008) (19)
- On a diophantine equation related to a conjecture of Erdös and Graham (2007) (19)
- Palindromes in Lucas Sequences (2003) (19)
- ON THE DIOPHANTINE EQUATION x2 + C = 2yn (2009) (18)
- Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields (2005) (18)
- On Fibonacci numbers with few prime divisors (2005) (18)
- On the proportion of numbers coprime to a given integer (2008) (18)
- On Pillai's Diophantine equation. (2006) (18)
- On the average number of divisors of the Euler function (2007) (18)
- Squares in Lehmer sequences and some Diophantine applications (2001) (17)
- Divisibility of Class Numbers: Enumerative Approach (2004) (17)
- Catalan and Apéry numbers in residue classes (2006) (17)
- ON THE DIOPHANTINE EQUATION x2 + 2a · 5b = yn (2008) (17)
- Fibonacci numbers which are sums of three factorials (2010) (17)
- Repdigits as sums of three Pell numbers (2018) (17)
- INTEGERS : ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 ( 2008 ) , # A 06 ON TOTIENT ABUNDANT NUMBERS (2008) (16)
- On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves (2011) (16)
- On the Greatest Common Divisor of u − 1 and v − 1 with u and v Near ${\cal S}$-units (2005) (16)
- On the radical of a perfect number (2010) (16)
- On a problem of Diophantus with polynomials (2007) (16)
- On Giuga numbers (2009) (16)
- MEMBERS OF LUCAS SEQUENCES WHOSE EULER FUNCTION IS A POWER OF 2 (2014) (16)
- Repdigits as sums of four Pell numbers (2019) (16)
- On the x-coordinates of Pell equations which are Fibonacci numbers II (2017) (16)
- Average multiplicative orders of elements modulo n (2003) (15)
- Repdigits as sums of two $$k$$k-Fibonacci numbers (2015) (15)
- Some additive combinatorics problems in matrix rings (2009) (15)
- Distribution of residues modulo p (2007) (15)
- Fibonacci Numbers which are Products of two Pell Numbers (2017) (15)
- On the largest prime factor of the mersenne numbers (2007) (15)
- $p$-adic quotient sets (2016) (15)
- ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2 (2017) (15)
- On the lower bound of the linear complexity over F/sub p/ of Sidelnikov sequences (2006) (15)
- Repdigits in k-Lucas sequences (2014) (15)
- On a generalization of the Pell sequence (2020) (15)
- The product of like-indexed terms in binary recurrences (Diophantine Problems and Analytic Number Theory) (2002) (15)
- Pell and Pell–Lucas Numbers as Sums of Two Repdigits (2020) (14)
- On the Exponential Local-Global Principle (2013) (14)
- On the exponential Diophantine equation Pxn+Pxn+1=Pm (2019) (14)
- ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn (2008) (14)
- On the largest prime factor of x2-1 (2010) (14)
- Lucas Diophantine Triples (2009) (14)
- On binary palindromes of the form 10n±1⁎ (2008) (14)
- ON STABLE QUADRATIC POLYNOMIALS (2012) (14)
- A note on odd perfect numbers (2011) (14)
- On an diophantine equation (2000) (14)
- On the x–coordinates of Pell equations which are k–generalized Fibonacci numbers (2018) (14)
- Diophantine m-tuples for primes (2005) (14)
- A quantitative lower bound for the greatest prime factor of $(ab+1)(bc+1)(ca+1)$ (2004) (14)
- The rth Moment of the Divisor Function: An Elementary Approach (2017) (13)
- Perfect Cuboids and Perfect Square Triangles (2000) (13)
- A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS FOR PURE POWERS (2008) (13)
- On an arithmetic function considered by Pillai (2009) (13)
- Power values of palindromes (2009) (13)
- Cullen Numbers with the Lehmer Property (2011) (13)
- Multiply perfect numbers in Lucas sequences with odd parameters (2001) (13)
- On the diophantine equation x 2 + 2 α 5 β 13 γ = y n (2008) (13)
- The negative Pell equation and Pythagorean triples (2000) (13)
- Palindromes in linear recurrence sequences (2013) (13)
- On the Value Set of n! Modulo a Prime (2005) (13)
- On the Number of Factorizations of an Integer (2016) (13)
- The diophantine equation x 2 = p a p b + 1 (2004) (13)
- On the X-coordinates of Pell equations which are rep-digits, II (2019) (12)
- Power of Two as sums of Three Pell Numbers (2016) (12)
- Prime Divisors of Shifted Factorials (2005) (12)
- On Pillai’s problem with the Fibonacci and Pell sequences (2018) (12)
- Uniform Distribution of Fractional Parts Related to Pseudoprimes (2005) (12)
- Composition Factors from the Table of Marks (2001) (12)
- Repdigits as Sums of Four Fibonacci or Lucas Numbers (2018) (12)
- On the diophantine equation x(2) + C=2y(n) (2009) (12)
- An explicit bound for the number of partitions into roots (2016) (12)
- On the system of Diophantine equations $a^2+b^2=(m^2+1)^r$ and $a^x+b^y=(m^2+1)^z$ (2012) (12)
- The range of the sum-of-proper-divisors function (2015) (12)
- On equal values of power sums of arithmetic progressions (2012) (12)
- Irreducible components and isomorphisms of the Burnside ring (2008) (12)
- Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields (2007) (12)
- On the counting function of irregular primes (2015) (12)
- Values of the Euler Function in Various Sequences (2005) (12)
- Multiperfect numbers with identical digits (2011) (12)
- Small exponent point groups on elliptic curves (2006) (11)
- Arithmetic properties of positive integers with fixed digit sum (2006) (11)
- Fibonacci numbers that are not sums of two prime powers (2005) (11)
- On the maximal order of numbers in the (2005) (11)
- Diophantine Triples and k-Generalized Fibonacci Sequences (2016) (11)
- Recurrence relations for polynomials obtained by arithmetic functions (2019) (11)
- Fermat Primes and Heron Triangles with Prime Power Sides (2003) (11)
- SETS WITH PRESCRIBED ARITHMETIC DENSITIES (2008) (11)
- On a variant of Giuga numbers (2011) (11)
- Repunit Lehmer numbers (2010) (11)
- A Diophantine equation in $k$-Fibonacci numbers and repdigits (2018) (11)
- On certain sums concerning the gcd’s and lcm’s of k positive integers (2018) (11)
- There are No Multiply-Perfect Fibonacci Numbers (2011) (11)
- ON THE GALOIS GROUP OF THE GENERALIZED FIBONACCI POLYNOMIAL (2001) (11)
- Some results on Oppenheim's ``Factorisatio Numerorum'' function (2010) (11)
- Quadratic Non-Residues Versus Primitive Roots Modulo p (2008) (11)
- Coincidences in the values of the Euler and Carmichael functions (2006) (11)
- ARITHMETIC FUNCTIONS OF FIBONACCI NUMBERS (2010) (10)
- The average Smarandache function (2001) (10)
- Integer Roots Chromatic Polynomials of Non-Chordal Graphs and the Prouhet-Tarry-Escott Problem (2005) (10)
- Euler indicators of binary recurrence sequences (2002) (10)
- On Pillai's problem with Pell numbers and powers of 2 (2019) (10)
- Representing integers as linear combinations of $S$-units (2009) (10)
- On the greatest common divisor of two Cullen numbers (2003) (10)
- Equations with arithmetic functions of Pell numbers (2014) (10)
- Some Diophantine equations from finite group theory: $\Phi_m (x) = 2p^n -1$ (2009) (10)
- Diophantine equations with products of consecutive terms in Lucas sequences II (2008) (10)
- X-coordinates of Pell equations as sums of two tribonacci numbers (2018) (10)
- An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers (2018) (10)
- On some conjectures on the monotonicity of some combinatorial sequences (2012) (10)
- On f(n) modulo Ω(n) and ω(n) when f is a polynomial (2004) (9)
- Arithmetic properties of members of a binary recurrent sequence (2003) (9)
- Common values of generalized Fibonacci and Pell sequences (2021) (9)
- PSEUDOPRIME CULLEN AND WOODALL NUMBERS (2007) (9)
- On integrality and periodicity of the Motzkin numbers (2005) (9)
- On the largest prime factor of n! + 2 n 1 (2005) (9)
- Compositions of n Satisfying Some Coprimality Conditions (2012) (9)
- On a question of G. Kuba (2000) (9)
- On the diophantine equation x2 + 2a · 3b · 11c = yn (2012) (9)
- On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers (2012) (9)
- On cyclotomic factors of polynomials related to modular forms (2019) (9)
- Tribonacci Diophantine quadruples (2015) (9)
- The Number of Non-Zero Digits of n! (2002) (9)
- Polynomial values of sums of products of consecutive integers (2018) (9)
- On the distribution of some means concerning the Euler function. (2008) (9)
- Irrationality of Power Series for Various Number Theoretic Functions (2005) (9)
- On the Diophantine equation x^2+2^a.3^b.11^c=y^n (2012) (9)
- X-coordinates of Pell equations which are Lucas numbers (2018) (9)
- Equations Involving Arithmetic Functions of Factorials (2000) (9)
- Lucas numbers as sums of two repdigits (2019) (9)
- Concatenations with Binary Recurrent Sequences (2005) (8)
- Linear independence of certain Lambert series (2014) (8)
- On the prime power factorization of n (2003) (8)
- Products of factorials modulo $p$ (2001) (8)
- Algebraic independence of infinite products generated by Fibonacci and Lucas numbers (2014) (8)
- The Anti-Social Fermat Number (2000) (8)
- The image of Carmichael’s λ-function (2014) (8)
- The divisor problem for d4 (n) in short intervals (2006) (8)
- Only finitely many Tribonacci Diophantine triples exist (2015) (8)
- Uniform distribution of the fractional part of the average prime divisor (2005) (8)
- On quadratic fields generated by polynomials (2008) (8)
- On the period of the continued fraction expansion of √22n+1 + 1 (2005) (8)
- Two Diophantine approaches to the irreducibility of certain trinomials (2007) (8)
- Cyclotomic coefficients: gaps and jumps (2015) (8)
- On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}=y^{n}$ (2009) (8)
- Control of coupled parabolic systems and Diophantine approximations (2013) (8)
- On the $g$-ary expansions of middle binomial coefficients and Catalan numbers (2011) (8)
- Fibonacci factoriangular numbers (2017) (8)
- On the Counting Function of Elliptic Carmichael Numbers (2012) (8)
- On the typical size and cancellations among the coefficients of some modular forms (2013) (8)
- Infinite families of noncototients (2000) (8)
- Repdigits as sums of three Lucas numbers (2019) (8)
- COMBINATORIAL DIOPHANTINE EQUATIONS AND A REFINEMENT OF A THEOREM ON SEPARATED VARIABLES EQUATIONS (2012) (8)
- On arithmetic lattices in the plane (2016) (8)
- Arithmetic properties of the Ramanujan function (2006) (8)
- On the largest prime factor of the ratio of two generalized Fibonacci numbers (2015) (8)
- On the Middle Prime Factor of an Integer (2013) (7)
- On the binary expansion of the odd Catalan numbers (2010) (7)
- On digit sums of multiples of an integer (2009) (7)
- ON GROUPS WITH PERFECT ORDER SUBSETS (2012) (7)
- On the X-coordinates of Pell equations which are products of two Fibonacci numbers (2019) (7)
- Diophantine triples of Fibonacci numbers (2016) (7)
- Exponential sums with Catalan numbers and middle binomial coefficients (2007) (7)
- Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function (2006) (7)
- On the difference in values of the Euler totient function near prime arguments (2017) (7)
- Class groups of quadratic fields of 3-rank at least 2: Effective bounds (2008) (7)
- EXPONENTS OF CLASS GROUPS OF REAL QUADRATIC FIELDS (2008) (7)
- Two divisors of $(n^2+1)/2$ summing up to $n+1$ (2007) (7)
- Cullen Numbers in Binary Recurrent Sequences (2004) (7)
- On squares in polynomial products (2010) (7)
- Arithmetic functions with linear recurrence sequences (2007) (7)
- The zero-multiplicity of third-order linear recurrences associated to the Tribonacci sequence (2014) (7)
- Coincidences in generalized Lucas sequences (2014) (7)
- On the zero–multiplicity of a fifth-order linear recurrence (2019) (7)
- On Integers for Which the Sum of Divisors is the Square of the Squarefree Core (2012) (7)
- Primitive Root Bias for Twin Primes (2017) (7)
- On the length of arithmetic progressions in linear combinations of S-units (2010) (7)
- Acknowledgment of priority: “On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions $\phi$ and $\sigma$” (Colloq. Math. 92 (2002), 111–130) (2012) (7)
- Values of arithmetical functions equal to a sum of two squares (2005) (7)
- Sierpinski and Carmichael numbers (2014) (7)
- On the spacings between C-nomial coefficients (2010) (7)
- Prime divisors of binary holonomic sequences (2008) (7)
- On members of Lucas sequences which are products of factorials (2019) (6)
- On the exact degree of Q (2010) (6)
- On the fixed points of the map $x \mapsto x^x$ modulo a prime, II (2014) (6)
- ON THE DIVERGENCE OF THE SMARANDACHE HARMONIC SERIES (1999) (6)
- Integers Divisible by the Sum of their Prime Factors (2005) (6)
- Sylvester's Theorem and the Non-integrality of a certain Binomial Sum (2015) (6)
- Total multiplicity of the Tribonacci sequence (2020) (6)
- Diophantine equations involving some classical counting functions (2013) (6)
- On Cullen numbers which are both Riesel and Sierpiński numbers (2012) (6)
- x-Coordinates of Pell equations which are Tribonacci numbers II (2018) (6)
- Zeckendorf representations with at most two terms to x-coordinates of Pell equations (2018) (6)
- On the range of Carmichael's universal-exponent function (2014) (6)
- The Orbit Problem for Parametric Linear Dynamical Systems (2021) (6)
- On Machin’s formula with powers of the golden section (2009) (6)
- Diophantine quadruples in the sequence of shifted Tribonacci numbers (2015) (6)
- On the local behavior of the order of appearance in the Fibonacci sequence (2014) (6)
- An arithmetic function arising from Carmichael’s conjecture (2011) (6)
- Repdigits as Euler functions of Lucas numbers (2016) (6)
- On the Euler function of repdigits (2008) (6)
- ON A DIOPHANTINE EQUATION OF CASSELS (2005) (6)
- Character sums and products of factorials modulo $p$ (2005) (6)
- On the values of the divisor function (2008) (6)
- Diversity in Parametric Families of Number Fields (2016) (6)
- On the Fixed Points of the Map x -> x^x Modulo a Prime (2014) (6)
- On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers (2010) (6)
- Visual properties of generalized Kloosterman sums (2015) (6)
- Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n (2006) (6)
- Power Totients with Almost Primes (2011) (6)
- ON VALUES OF d(n!)/m!, ϕ(n!)/m! AND σ(n!)/m! (2010) (6)
- Residue classes having tardy totients (2007) (6)
- On the diophantine equation ²=4^{}-4ⁿ+1 (2002) (6)
- On the sum of the first $n$ values of the Euler function (2014) (6)
- ON THE IRRATIONALITY OF A DIVISOR FUNCTION SERIES (2007) (5)
- Binary polynomial power sums vanishing at roots of unity (2020) (5)
- On quadratic fields generated by the Shanks sequence (2009) (5)
- Trinomials with given roots (2019) (5)
- Multiplicative Independence in k-Generalized Fibonacci Sequences (2016) (5)
- on the value set of the Carmichael λ-function (2007) (5)
- Short interval asymptotics for a class of arithmetic functions (2006) (5)
- Remarks on a Sequence of Minimal Niven Numbers (2007) (5)
- On the equation $x^2+dy^2=F_n$ (2007) (5)
- Carmichael numbers in the sequence (2n k+1)n≥1 (2015) (5)
- On Some Conjectures on the Monotonicity of Some Arithmetical Sequences (2012) (5)
- On Positivity and Minimality for Second-Order Holonomic Sequences (2020) (5)
- On Pillai's problem with X-coordinates of Pell equations and powers of 2 (2019) (5)
- On the sum of digits of some sequences of integers (2012) (5)
- On the diophantine equation px1 − px2 = qy1 − qy2 (2003) (5)
- A Remark on Prime Divisors of Lengths of Sides of Heron Triangles (2003) (5)
- On the diophantine equation x2 = 4qm - 4qn+ 1 (2003) (5)
- Integers divisible by sums of powers of their prime factors (2008) (5)
- How often is n! a sum of three squares? (2010) (5)
- On the nonnegative integer solutions to the equation F ± F = y (2021) (5)
- On the Distribution of Perfect Totients (2006) (5)
- Galois Groups of Polynomials Arising from Circulant Matrices (2008) (5)
- Pseudoprime reductions of elliptic curves (2009) (5)
- On the discriminator of Lucas sequences (2017) (5)
- Primitive root biases for prime pairs I: existence and non-totality of biases (2017) (5)
- Arithmetic properties of Apéry numbers (2008) (5)
- On the least common multiple of Lucas subsequences (2013) (5)
- On shifted products which are powers (2005) (5)
- TWISTED EXTENSIONS OF THE CUBIC CASE OF FERMAT’S LAST THEOREM (2010) (5)
- On the sumset of the primes and a linear recurrence (2013) (5)
- Prime factors of Motzkin numbers (2006) (5)
- Diophantine Approximations and a Problem from the 1988 IMO (2006) (5)
- On strings of consecutive integers with a distinct number of prime factors (2008) (5)
- On the moments of the Carmichael λ function (2006) (5)
- On finite fields for pairing based cryptography (2007) (5)
- On numbers n for which the prime factors of σ(n) are among the prime factors of n (2004) (5)
- Rectangles Of Nonvisible Lattice Points (2015) (5)
- Some remarks on Sierpinski numbers and related problems (2009) (5)
- Integers without divisors from a fixed arithmetic progression (2006) (5)
- Common factors of shifted Fibonacci numbers (2003) (5)
- A note on the number of $S$-Diophantine quadruples (2014) (5)
- On the Equation $y^x\pm x^y=z^2$ (2000) (4)
- THE MULTIPLICATIVE GROUP GENERATED BY THE LEHMER NUMBERS (2010) (4)
- On Diophantine quadruples of Fibonacci numbers (2017) (4)
- Uniformity of distribution modulo 1 of the geometric mean prime divisor (2006) (4)
- On a compositeness test for (2 p + 1)/3 (2010) (4)
- Counting dihedral and quaternionic extensions (2011) (4)
- Errata to "On the largest prime factor of x2-1" (2013) (4)
- Prime factors of a f (n) − 1 with an irreducible polynomial f (x) (2006) (4)
- On the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn (2008) (4)
- Irreducible Components of the Burnside Ring (2005) (4)
- On the Diophantine Equation $x^4-q^4 = py^3$ (2010) (4)
- On the Diophantine equation $F_n^x+F_{n+1}^x=F_m^y$ (2015) (4)
- On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ (2000) (4)
- Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function (2019) (4)
- On the Skolem Problem and the Skolem Conjecture (2022) (4)
- On a problem of Nicol and Zhang (2008) (4)
- On the number of nonquadratic residues which are not primitive roots (2004) (4)
- On the positive integral solutions of the Diophantine equation . (2008) (4)
- On the Lower Bound of the Linear Complexity Over of (2006) (4)
- Products of factorials in Smarandache type expressions (1997) (4)
- On the Fürstenberg closure of a class of binary recurrences (2010) (4)
- LINEAR INDEPENDENCE OF POWERS OF SINGULAR MODULI OF DEGREE THREE (2017) (4)
- Pell numbers with the Lehmer property (2015) (4)
- Multiperfect numbers on lines of the Pascal triangle (2009) (4)
- On the solutions of the Diophantine equation Fn±a(10m−1)9=k! (2022) (4)
- On the degree of compositum of two number fields (2013) (4)
- POWERFUL NUMBERS IN SHORT INTERVALS (2005) (4)
- On the equation ?(?(n))=?(n)+k$ (2007) (4)
- Distribution of harmonic sums and Bernoulli polynomials modulo a prime (2006) (4)
- Estimates for Wieferich numbers (2007) (4)
- Groups with two Sylow numbers are solvable (1998) (4)
- Sums of prime divisors and Mersenne numbers (2007) (4)
- Waring problem with factorials (2005) (4)
- On the values of a class of analytic functions at algebraic points (2008) (4)
- The distribution of integers n divisible by lω(n) (2004) (4)
- Fermat numbers in the Pascal triangle. (2001) (4)
- On the Complexity of Testing Elite Primes (2011) (4)
- Lucas Numbers with Lehmer Property (2015) (4)
- The x-coordinates of Pell equations and sums of two Fibonacci numbers II (2020) (4)
- Products of $k$-Fibonacci numbers which are rep-digits (2020) (4)
- PRIME DIVISORS OF LUCAS SEQUENCES AND A CONJECTURE OF SKAŁBA (2005) (4)
- On the Euler Function of Fibonacci Numbers (2009) (4)
- Linear combinations of prime powers in X-coordinates of Pell equations (2020) (4)
- On the zero-multiplicity of the k-generalized Fibonacci sequence (2020) (4)
- On the Diophantine equation 2m+nx2=yn (2012) (4)
- On a Divisibility Property Involving Factorials (2000) (4)
- On a Divisibility Relation for Lucas Sequences (2015) (4)
- Pseudoprimes in certain linear recurrences (2007) (4)
- Product of Consecutive Tribonacci Numbers With Only One Distinct Digit (2019) (4)
- Integers representable as the sum of powers of their prime factors (2005) (4)
- Power of Two--Classes in k--Generalized Fibonacci Sequences (2014) (4)
- On the distance between generalized Fibonacci numbers (2015) (4)
- On the composition of the Euler function and the sum of divisors function (2007) (4)
- ON THE RANGE OF THE ITERATED EULER FUNCTION (2008) (3)
- On the Multiplicative Order of Fn+1/Fn Modulo Fm (2013) (3)
- On the composition of a certain arithmetic function (2009) (3)
- On the system of Diophantine equations (m2−1)r+b2=c2 and (m2−1)x+by=cz (2015) (3)
- On barycentric constants (2012) (3)
- The Euler Function of Fibonacci and Lucas Numbers and Factorials (2013) (3)
- Arithmetic properties of the sum of the first $$n$$n values of the Euler function (2015) (3)
- ON THE SUMS OF COMPLEMENTARY DIVISORS (2007) (3)
- Factors of Fermat Numbers (2002) (3)
- On the sum of divisors of the Mersenne numbers (2003) (3)
- ON A VARIATION OF A CONGRUENCE OF SUBBARAO (2012) (3)
- Divisibility properties of binary recurrent sequences (2001) (3)
- Products of members of Lucas sequences with indices in an interval being a power (2009) (3)
- On perfect numbers which are ratios of two Fibonacci numbers ∗ (2010) (3)
- On numbers not of the form n -?( n (2005) (3)
- On a Diophantine equation involving powers of Fibonacci numbers (2020) (3)
- On the Diophantine Equation x 2 +2 alpha 5 beta 13 gamma =y n . (2008) (3)
- On the number of nonzero digits of the partition function (2012) (3)
- Collinear CM-points (2015) (3)
- On the sum of two divisors of (n2 + 1)/2 (2012) (3)
- Variants of the Brocard-Ramanujan equation (2008) (3)
- On integers with a special divisibility property (2006) (3)
- Markov Type Equations with Solutions in Lucas Sequences (2021) (3)
- On the solutions of the congruence ²≡1(²()) (2001) (3)
- On the formula Fp = u2 + pv2 (2015) (3)
- Consecutive binomial coefficients satisfying a quadratic relation (2006) (3)
- Algebraic results for the values 𝜗3(mτ) and 𝜗3(nτ) of the Jacobi theta-constant (2019) (3)
- A Generalization of a Theorem of Cohn on the Equation $x^3-Ny^2=\pm1$ (2001) (3)
- φ(Fn ) = Fm (2009) (3)
- ON SUMS OF FIBONACCI NUMBERS MODULO p (2011) (3)
- Multiplicative relations on binary recurrences (2013) (3)
- IRRATIONALITY OF LAMBERT SERIES ASSOCIATED WITH A PERIODIC SEQUENCE (2014) (3)
- On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind (2003) (3)
- On the local behavior of the Carmichael λ-functions (2006) (3)
- Counting Keith numbers (2006) (3)
- On the non-trivial cycles in Collatz’s problem (2005) (3)
- On positive integers n such that Phi(1)+Phi(2)+... +Phi(n) is a square (2008) (3)
- On the sum of the first n primes being a square (2007) (3)
- Digit sums of binomial sums (2012) (3)
- Correction to: X-coordinates of Pell equations as sums of two Tribonacci numbers (2019) (3)
- Asymptotic formulas for certain arithmetic functions (2008) (3)
- Compositions with the euler and carmichael functions (2005) (3)
- Perfect repdigits (2013) (3)
- Skolem Meets Schanuel (2022) (3)
- Pillai’s problem with the Fibonacci andPadovan sequences (2019) (3)
- Universal Skolem Sets (2021) (3)
- On composite integers n for which '(n) j n 1 (2009) (3)
- SOME DIVISIBILITY PROPERTIES OF THE EULER FUNCTION (2005) (3)
- On the size of sets whose elements have perfect power n-shifted products (2011) (3)
- On Y-coordinates of Pell equations which are base 2 rep-digits (2020) (3)
- On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers (2013) (3)
- Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms (2017) (3)
- Another Note on the Greatest Prime Factors of Fermat Numbers (2001) (3)
- On a Diophantine equation involving Fibonacci numbers and the Ramanujan $$\tau $$ τ -function of factorials (2022) (3)
- On the formula Fp = u2 + pv2 (2015) (3)
- On integers which are not differences of two powers (2002) (3)
- Perfect powers in Smarandache type expressions (1997) (3)
- The Number of Solutions of λ(x) = n (2011) (2)
- Binomial Coefficients and Lucas Sequences (2002) (2)
- Corrigendum to “Coincidences in generalized Fibonacci sequences” [J. Number Theory 133 (6) (2013) 2121–2137] (2013) (2)
- On cyclic compositions of positive integers (2011) (2)
- Infinite sets of positive integers whose sums are free of powers (2002) (2)
- On the exact degree of ℚ(√₁,√₂,...,√_{ℓ}) over ℚ (2010) (2)
- On the largest prime factor of numerators of Bernoulli numbers (2012) (2)
- Counting permutation equivalent degree six binary polynomials invariant under the cyclic group (2016) (2)
- Roughly squarefree values of the Euler and Carmichael functions (2005) (2)
- ON THE SUM OF THE FIRST n PRIMES (2007) (2)
- On the independence of $\sigma (\phi (n))$ and $\phi (\sigma (n))$ (2009) (2)
- Problems: 10620-10626 (1997) (2)
- Variants of the Diophantine equation n! + 1 = y2 (2010) (2)
- Constrained ternary integers (2017) (2)
- Diophantine triples in linear recurrences of Pisot type (2017) (2)
- Corrigendum to ‘‘Positive integers divisible by the product of their nonzero digits’’, Portugaliae Math. 64 (2007), 1: 75–85 (2017) (2)
- On the fractional parts of an/n (2013) (2)
- ON THE INDEX OF COMPOSITION OF THE EULER FUNCTION AND OF THE SUM OF DIVISORS FUNCTION (2009) (2)
- A Generalization of a Lemma of Sullivan (2012) (2)
- On the number of divisors of n! and of the Fibonacci numbers (2012) (2)
- Some Diophantine equations from flnite group theory: 'm(x) = 2p n ¡ 1 (2011) (2)
- Algebraic Model Checking for Discrete Linear Dynamical Systems (2022) (2)
- On Y -coordinates of Pell equations which are members of a fixed binary recurrence (2020) (2)
- On the prime factors of the iterates of the Ramanujan τ–function (2020) (2)
- Positive integers divisible by the product of their nonzero digits (2007) (2)
- Positive Integers Whose Euler Function Is a Power of Their Kernel Function (2006) (2)
- An elliptic sequence is not a sampled linear recurrence sequence (2016) (2)
- ON POLYNOMIALS WHOSE ROOTS HAVE RATIONAL QUOTIENT OF DIFFERENCES (2017) (2)
- Big prime factors in orders of elliptic curves over finite fields (2021) (2)
- ON THE EQUATION (5 m - 1) = 5 n - 1 (2015) (2)
- On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2 (2018) (2)
- Denominators of Bernoulli polynomials (2017) (2)
- On a conjecture of Erdos and Stewart (2000) (2)
- Lucas factoriangular numbers (2018) (2)
- Composite positive integers with an average prime factor (2007) (2)
- On the Sum of Divisors of Binomial Coefficients (2010) (2)
- Power Values of Divisor Sums (2012) (2)
- On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences (2020) (2)
- On the Oppenheim's "factorisatio numerorum" function (2008) (2)
- Trinomials, singular moduli and Riffaut's conjecture (2020) (2)
- Generalized poly-Cauchy polynomials and their interpolating functions (2014) (2)
- Members of binary recurrences on lines of the Pascal triangle (2005) (2)
- Pell Numbers whose Euler Function is a Pell Number (2015) (2)
- Perfect powers with all equal digits but one. (2005) (2)
- Sums of divisors of Fibonacci numbers (2009) (2)
- On Multiplicative Magic Squares (2010) (2)
- ON A CONJECTURE OF BROUGHAN (2007) (2)
- On ternary Egyptian fractions with prime denominator (2019) (2)
- ON THE PRODUCT OF DIVISORS OF n AND OF σ(n) (2003) (2)
- On Fibonacci Numbers Which Are Elliptic Korselt Numbers (2014) (2)
- Number fields in fibers: the geometrically abelian case with rational critical values (2016) (2)
- On the number of non-zero digits of integers in multi-base representations (2017) (2)
- Nonaliquots and Robbins numbers (2005) (2)
- On the error term of a lattice counting problem (2017) (2)
- EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FIBONACCI AND LUCAS NUMBERS (1998) (2)
- ON THE SQUARE-FREE PARTS OF ⌊en!⌋ (2007) (2)
- On a conjecture concerning the multiplicity of the Tribonacci sequence (2020) (2)
- Fibonacci Numbers with Prime Sums of Complementary Divisors (2014) (2)
- On the exact degree of $\mathbb {Q}(\sqrt {a_1}, \sqrt {a_2},…, \sqrt {a_\ell })$ over $\mathbb {Q}$ (2010) (2)
- On two functions arising in the study of the Euler and Carmichael quotients (2017) (2)
- On a conjecture of Ma (2005) (2)
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm (2020) (2)
- On the Euler function of the Catalan numbers (2012) (2)
- Arithmetic functions monotonic at consecutive arguments (2014) (2)
- ON PERFECT POWERS IN LUCAS SEQUENCES (2005) (2)
- Pell factoriangular numbers (2019) (2)
- Aliquot Cycles of Repdigits (2011) (2)
- Some Diophantine equations from finite group theory : Φ (2010) (2)
- MONOTONIC PHINOMIAL COEFFICIENTS (2017) (2)
- Some remarks on the values of the Riemann zeta function and Bernoulli numbers (2012) (2)
- Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials (2017) (2)
- On some monotonic combinatorial sequences conjectures (2012) (2)
- Diophantine triples with values in the sequences of Fibonacci and Lucas numbers (2017) (2)
- On the Parity of the Number of Small Divisors of n (2015) (1)
- On Numbers of the Form p + 2n - n (2014) (1)
- Primitive root discrepancy for twin primes (2017) (1)
- A Number and Its Totient Are Not Amicable: 10793 (2002) (1)
- Fibonacci numbers as sums of two Padovan numbers (2022) (1)
- GAPS IN BINARY EXPANSIONS OF SOME ARITHMETIC FUNCTIONS, AND THE IRRATIONALITY OF THE EULER CONSTANT (2012) (1)
- k{generalized Fibonacci numbers of the form (2014) (1)
- On the Densities of Some Subsets of Integers (2007) (1)
- On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime (2022) (1)
- Partial Sums of Powers of Prime Factors (2007) (1)
- On square values of the product of the Euler totient and sum of divisors functions (2013) (1)
- On the exponential Diophantine equation P xn + P xn (2019) (1)
- Multiplicatively dependent triples of Tribonacci numbers (2015) (1)
- On a binary recurrent sequence of polynomials (2015) (1)
- Diophantine $$\mathcal{S} $$S-quadruples with two primes which are twin (2019) (1)
- Repdigit Keith numbers (2013) (1)
- Class numbers with many prime factors (2008) (1)
- A VARIATION ON THE THEME OF NICOMACHUS (2017) (1)
- A Universal Skolem Set of Positive Lower Density (2022) (1)
- Consecutive Integers with Close Kernels (2018) (1)
- Three essays on Machin's type formulas (2023) (1)
- On the equation φ(Xm - 1) = Xn - 1 (2015) (1)
- Fibonacci and Lucas numbers as difference of two repdigits (2021) (1)
- Standard Noether normalizations of the graph subring (2006) (1)
- Ratios of sums of two Fibonacci numbers equal to powers of 2 (2020) (1)
- POSITIVE INTEGERS n SUCH THAT n|a σ(n) − 1 (2003) (1)
- Composite positive integers whose sum of prime factors is prime (2020) (1)
- Terms of Lucas sequences having a large smooth divisor (2022) (1)
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem (2010) (1)
- Prime Divisors Of Some Recurrence Sequence (2007) (1)
- Romanov type problems (2018) (1)
- X-coordinates of Pell equations as sums of two tribonacci numbers (2017) (1)
- Mackey Functors with Chain Conditions (1998) (1)
- Uniform distribution of some ratios involving the number of prime and integer divisors (2006) (1)
- On a problem of Pillai with Fibonacci numbers and powers of 2 (2017) (1)
- Prime divisors of some shifted products (2005) (1)
- Linear independence results for the reciprocal sums of Fibonacci numbers associated with Dirichlet characters (2017) (1)
- On the Exponential Diophantine Equation F xn +1 − F xn − 1 = F ym (2022) (1)
- Counting terms $U_n$ of third order linear recurrences with $U_n=u^2+nv^2$ (2015) (1)
- An inequality for Fibonacci numbers (2022) (1)
- On the Fibonacci distances of ab, ac and bc (2013) (1)
- Arithmetic properties of coefficients of L-functions of elliptic curves (2018) (1)
- On the largest prime factor of the partition function of n (2012) (1)
- Amicable Pell numbers. (2002) (1)
- Positive integers such that . (2003) (1)
- Perfect Pell and Pell–Lucas numbers (2019) (1)
- Aliquots sums of Fibonacci numbers (2010) (1)
- On the solutions of the congruence n^2 ¿ 1 (mod phi^2 (n)) (2001) (1)
- Diophantine equations involving factorials (2017) (1)
- Multiplicative dependence between k-Fibonacci and k-Lucas numbers (2020) (1)
- On the Diophantine equation $x^4-q^4=py^r$ (2011) (1)
- Quadratic forms representing the $p$-th Fibonacci number (2015) (1)
- On the equation ∑j=1kjFjp=Fnq (2020) (1)
- On the diophantine equation $2^x=x^2+y^2-2$ (2012) (1)
- Perfect squares representing the number of rational points on elliptic curves over finite field extensions (2020) (1)
- Pentagonal and heptagonal repdigits (2020) (1)
- Binary recurrences for which powers of two are discriminating moduli (2020) (1)
- Can Two Consecutive Numbers Both Be Perfect?: 10711 (2001) (1)
- On a Series Involving S(1) ·S(2) ... ·S(n) (2014) (1)
- The zero-multiplicity of Berstel type sequences (2019) (1)
- LINEAR DIOPHANTINE EQUATION WITH THREE CONSECUTIVE BINOMIAL COEFFICIENTS (2004) (1)
- Linear combinations of factorial and S-unit in a ternary recurrence sequence with a double root (2022) (1)
- Linear equations with the Euler totient function (2007) (1)
- Bounding the number of solutions of some congruences (2005) (1)
- On Pillai’s problem with X-coordinates of Pell equations and powers of 2 II (2021) (1)
- On the equation \ x^y\pm y^x=\prod n_i! (2000) (1)
- Finiteness results for Diophantine triples with repdigit values (2015) (1)
- Local Behavior of the Composition of the Aliquot and Co-Totient Functions (2016) (1)
- On the distribution of the Euler function with Fibonacci numbers (2011) (1)
- k-generalized Fibonacci numbers of the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k} (2014) (1)
- On fundamental units of real quadratic fields of class number 1 (2019) (1)
- THE DIOPHANTINE EQUATION Fyn + Fxn+1 = Fxm (2014) (1)
- Sometimes Divides σk(): 11090 (2006) (1)
- 121221222 ... Is Not Quadratic (2005) (1)
- On a nonintegrality conjecture (2021) (1)
- SOME REMARKS ON THE RIEMANN ZETA FUNCTION AND PRIME FACTORS OF NUMERATORS OF BERNOULLI NUMBERS (2011) (1)
- Minimal Niven numbers (2008) (1)
- On the Sum of Digits of Numerators of Bernoulli Numbers (2013) (1)
- The Most Beautiful Theorems on Fermat Numbers (2002) (1)
- On the Smarandache irrationality conjecture (2000) (1)
- On a problem of K. R. S. Sastry (2001) (1)
- UNIFORM DISTRIBUTION MODULO 1 OF THE HARMONIC PRIME FACTOR OF AN INTEGER (2010) (1)
- Markov triples with k-generalized Fibonacci components (2020) (1)
- Perfect powers in the summatory function of the power tower (2010) (1)
- On members of Lucas sequences which are products of Catalan numbers (2020) (1)
- Power Classes Of Recurrence Sequences (2004) (1)
- On the number of antipodal bicolored necklaces (2012) (1)
- A Journey through Galois Groups , Irreducible Polynomials and Diophantine Equations (2003) (1)
- An Equation Involving the Totient: 10626 (1999) (1)
- On the discriminator of Lucas sequences (2018) (1)
- Expansions of binary recurrences in the additive base formed by the number of divisors of the factorial (2014) (1)
- On special finite fields (2009) (1)
- O N NUMBERS OF THE FORM p + 2 n − n ∗ (2015) (1)
- On the $x$--coordinates of Pell equations that are products of two Pell numbers (2019) (1)
- On Sierpinski Numbers of the Form φ(N)/2n (2016) (1)
- FACTORIALS AND THE RAMANUJAN FUNCTION (2015) (1)
- On the Diophantine equation x4-q4 = pyr (2011) (1)
- A note on the denominators of Bernoulli numbers (2014) (1)
- On the separation of the roots of the generalized Fibonacci polynomial (2022) (1)
- On integers which are the sum of a power of 2 and a polynomial value (2014) (1)
- Product of repdigits with consecutive lengths in the Fibonacci sequence. (2021) (1)
- Some divisibilities amongst the terms of linear recurrences (2006) (1)
- On the equation 1k+2k+···+nk=x2 (2002) (1)
- On a result of Fujita and Le (2022) (0)
- Two b–repunits in the Fibonacci sequence (2021) (0)
- On positive integers with a certain nondivisibility property ∗ (2008) (0)
- On a Diophantine Equation of Stroeker (2010) (0)
- On the greatest prime factor of sides of a Heron triangle (2009) (0)
- Appendix. Basic complex analysis theory (2012) (0)
- Quadratic forms representing pth terms of Lucas sequences (2017) (0)
- φ and σ : from Euler to Erdős (2011) (0)
- Repdigit Keith numbers (2013) (0)
- On Positive Integers n with a Certain Divisibility Property (2009) (0)
- Divisibility of Fermat Numbers (2002) (0)
- Triangular numbers whose sum of divisors is also triangular (2007) (0)
- Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes (2002) (0)
- 2 Special Varieties and the Theorem of Pila (2015) (0)
- VSH and multiplicative modular relations between small primes with polynomial exponents (2014) (0)
- Arithmetic properties of the integer part of the powers of an algebraic number (2009) (0)
- Prime numbers in arithmetic progression (2012) (0)
- How many primes can divide the values of a polynomial (2012) (0)
- − 1 (2004) (0)
- On the $p$-adic zeros of the Tribonacci sequence (2022) (0)
- A Characterization of Certain Binary Recurrence Sequences (2001) (0)
- Additive Diophantine Equations with Binary Recurrences, $${{\mathcal {S}}}$$-Units and Several Factorials (2023) (0)
- VSH and multiplicative modular relations between small primes with polynomial exponents (2014) (0)
- L -polynomials of function ﬁelds and Fibonacci Numbers (2015) (0)
- Concatenating perfect powers (2013) (0)
- Perfect powers in q-binomial coefficients (2012) (0)
- Pseudoprime Reductions of Elliptic Curves – CORRIGENDUM (2012) (0)
- Duplications in the k-generalized Fibonacci sequences (2021) (0)
- On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers (2022) (0)
- On the proximity of large primes (2017) (0)
- On an equation of Goormaghtigh (2011) (0)
- des Nombres de Bordeaux 00 ( XXXX ) , 000 – 000 Almost Powers in the Lucas Sequence par (2008) (0)
- The Proof of Gauss’s Theorem (2002) (0)
- On the equation ( 2 k − 1 ) ( 3 ` − 1 ) = 5 m − 1 (2020) (0)
- On the exponential Diophantine equation $F_{n}^{x}+F_{n+1}^{x}+\cdots+F_{n+k-1}^{x}=F_{m}$ (2022) (0)
- The Diophantine equations P xn + P yn + 1 = P xm or P yn + P xn + 1 = P xm (2023) (0)
- On the sum of two divisors of (n2 + 1)/2 (2012) (0)
- Erratum to: On the length of arithmetic progressions in linear combinations of S-units (2014) (0)
- ADVANCED PROBLEMS AND SOLUTIONS (2010) (0)
- Diophantine triples with distinct binary recurrences (2022) (0)
- The number of solutions of lambda(x)=n (2010) (0)
- Markov triples with two Fibonacci components (2022) (0)
- A conjecture of Erdős concerning inequalities for the Euler totient function (2001) (0)
- Selected applications of primes in arithmetic progression (2012) (0)
- Proceedings of the Fourteenth International Conference on Fibonacci Numbers and Their Applications (2011) (0)
- Prime factors of af ( n ) − 1 with an irreducible polynomial f ( x ) Christian Ballot and (2006) (0)
- ERRATA TO "UNIFORM DISTRIBUTION OF SOME RATIOS INVOLVING THE NUMBER OF PRIME AND INTEGER DIVISORS", UDT 1 (2006), 15-26 (2011) (0)
- Fibonacci numbers as sums of two Padovan numbers (2022) (0)
- Control of coupled parabolic systems and Diophantine approximations (2013) (0)
- The proof of the prime number theorem (2012) (0)
- Coprime partitions and Jordan totient functions (2020) (0)
- Basic Properties of Fermat Numbers (2002) (0)
- X-coordinates of Pell equations which are Lucas numbers (2018) (0)
- On the Pillai-Tijdeman Diophantine equation involving terms of Lucas sequences (2021) (0)
- On numbers not of the form <Emphasis Type=”Italic”>n</Emphasis>-ω(<Emphasis Type=”Italic”>n</Emphasis>) (2005) (0)
- Number fields in fibers: the geometrically abelian case with rational critical values (2017) (0)
- A Note on r-Full Numbers of the Form lm + k (2000) (0)
- A note on the Diophantine Equation x^2-kxy+ky^2+ly=0 (2021) (0)
- Prime numbers and their properties (2012) (0)
- DIOPHANTINE S -QUADRUPLES WITH TWO PRIMES WHICH ARE TWIN (2019) (0)
- Diophantine quadruples with values in k-generalized Fibonacci numbers (2018) (0)
- Multiplicative Independence in k-Generalized Fibonacci Sequences (2016) (0)
- Exponential Diophantine Equations (2019) (0)
- On the iterates of shifted Euler's function (2023) (0)
- Program of the first international conference "Smarandache Type Notions in Number Theory" (2000) (0)
- Linear Equations with Euler Totient Functions (2007) (0)
- Corrigendum to “Cullen numbers with the Lehmer property” (2011) (0)
- Perfect Squares as Concatenation of Consecutive Integers (2019) (0)
- On cyclotomic factors of polynomials related to modular forms (2018) (0)
- On the Diophantine Equation x2+2alpha5beta13gamma=yn (2008) (0)
- Amicable pairs with few distinct prime factors (2016) (0)
- Irrationality of Infinite Series (2019) (0)
- Squares in a certain sequence related to L-functions of elliptic curves (2013) (0)
- On the divisibility Fk|Fx2 + Fx + 1 (2021) (0)
- On the Local Minima of the Order of Appearance Function (2015) (0)
- Generalizations of Fermat Numbers (2002) (0)
- N T ] 1 0 M ay 2 01 0 On the largest prime factor of x 2 − 1 (2010) (0)
- On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences (2021) (0)
- The Product of Exponents in the Factorization of Consecutive Integers (2009) (0)
- On the number of nonzero digits of the partition function (2012) (0)
- Euclidean Construction of the Regular Heptadecagon (2002) (0)
- ON THE LOG-CONCAVITY OF THE DEGENERATE BERNOULLI NUMBERS (2012) (0)
- Universität Stuttgart Fachbereich Mathematik Irreducible Components of the Burnside Ring (0)
- On the divisibility F k | F 2 x + F x + 1 (2020) (0)
- On (almost) realizable subsequences of linearly recurrent sequences (2022) (0)
- Pell numbers with the Lehmer property (2016) (0)
- On a recursively defined sequence involving the prime counting function (2020) (0)
- Pell and Pell–Lucas Numbers as Sums of Two Repdigits (2019) (0)
- Erratum to the Paper “Fibonacci Numbers with the Lehmer Property”(Bull. Polish Acad. Sci. Math. 55 (2007), 7–15) (2011) (0)
- Arithmetic properties of coefficients of L-functions of elliptic curves (2018) (0)
- Complete solution of the exponential Diophantine equation (2022) (0)
- ON THE LOG-CONCAVITY OF THE DEGENERATE BERNOULLI NUMBERS (2012) (0)
- On the multiplicative independence of the roots of generalized Fibonacci and Pell polynomials (2022) (0)
- On strings of consecutive economical numbers of arbitrary length (2005) (0)
- On a divisibility problem (2018) (0)
- Fibonacci lattice points (2010) (0)
- Generalized Lucas graphs (2023) (0)
- Elliptic curves over finite fields with Fibonacci numbers of points (2020) (0)
- The Irrationality of the Sum of Some Reciprocals (2002) (0)
- LUCAS SEQUENCES FOR WHICH (2004) (0)
- $$L$$L-polynomials of function fields and Fibonacci Numbers (2015) (0)
- Squares and factorials in products of factorials F (2013) (0)
- On the Srnarandache Irrationality Conjecture (2014) (0)
- Irrationality of Infinite Series (2019) (0)
- Diophantine triples in linear recurrences of Pisot type (2018) (0)
- When do the Fibonacci invertible classes modulo M form a subgroup (2012) (0)
- Average order in cyclic groups par (2002) (0)
- Powers of Rational Matrices (2021) (0)
- Numbers of the form kf(k) (2022) (0)
- On a sequence of integers arising from simultaneous Pell equations (2008) (0)
- Repdigits as sums of three Pell numbers (2018) (0)
- On Egyptian fractions of length 3 (2021) (0)
- Diophantine equations with products of consecutive members of binary recurrences (2017) (0)
- On equal values of products and power sums of consecutive elements in an arithmetic progression (2023) (0)
- # A 53 INTEGERS 11 ( 2011 ) ALIQUOT CYCLES OF REPDIGITS (2011) (0)
- The Diophantine Equation Fny + Fn+1x = Fmx (2013) (0)
- ON PRIME-PERFECT NUMBERS (2011) (0)
- Correction to: X-coordinates of Pell equations as sums of two Tribonacci numbers (2019) (0)
- Identities for the k-generalized Fibonacci sequence with negative indices and its zero-multiplicity (2022) (0)
- $\phi$ and $\sigma$: from Euler to Erd\H os (2011) (0)
- FINITENESS FOR DIOPHANTINE TRIPLES WITH REPDIGIT VALUES (2015) (0)
- On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$ (2004) (0)
- On the number of divisors of the least common multiples of shifted prime powers (2021) (0)
- Corrigendum to “Pentagonal and heptagonal repdigits” [Annales Mathematicae et Informaticae 52 (2020) 137–145] (2021) (0)
- The Beast and triangular Zeckendorf representations (2011) (0)
- The fascinating Euler function (2012) (0)
- A VARIANT ON THE NOTION OF A DIOPHANTINE s-TUPLE (2009) (0)
- Fermat Primes and a Diophantine Equation (2002) (0)
- Common Divisors of the Euler Function at Related Arguments (2011) (0)
- There are no Diophantine quadruples of Pell numbers (2021) (0)
- Characters and the Dirichlet theorem (2012) (0)
- A pr 2 00 3 On the prime power factorization of n ! (2003) (0)
- The Riemann zeta function (2012) (0)
- The index of composition of an integer (2012) (0)
- On the sum of the reciprocals of k-generalized Fibonacci numbers (2022) (0)
- A ug 2 01 9 PRIMITIVE ROOT BIAS FOR TWIN PRIMES II (2019) (0)
- On the Multiplicities of Padovan-Type Sequences (2022) (0)
- Congruent numbers with higher exponents (2006) (0)
- Problem 11090 (2004) (0)
- On a problem of Bednarek (2012) (0)
- Coincidences of Catalan and q-Catalan Numbers (2011) (0)
- On Fibonacci numbers which are elliptic Carmichael (2016) (0)
- A note on fibonomial coefficients (2019) (0)
- On lattice points where all nearby points are not relatively prime (2015) (0)
- Perfect powers in solutions to Pell equations (2009) (0)
- WHEN THE SUM OF ALIQUOTS DIVIDES THE TOTIENT (2007) (0)
- Euler to the Rescue: 10869 (2003) (0)
- On the gaps between q-binomial coefficients (2020) (0)
- Snapshots of Mathematics in Sub-Saharan Africa (2018) (0)
- Zeckendorf representations with at most two terms to x-coordinates of Pell equations (2019) (0)
- x-Coordinates of Pell equations which are Tribonacci numbers II (2018) (0)
- Additive Diophantine Equations with Binary Recurrences, S -Units and Several Factorials (2023) (0)
- On Y-coordinates of Pell equations which are Lucas numbers (2022) (0)
- Fermat Number Transform and Other Applications (2002) (0)
- On a variant of Giuga numbers (2011) (0)
- On Factorizations of Escalator Numbers (2007) (0)
- ON REPUNIT CULLEN NUMBERS (2022) (0)
- 84.38 Digital patterns in perfect squares (2000) (0)
- Additive properties of subgroups of finite index in fields (2011) (0)
- Small exponent point groups on elliptic curves par (2006) (0)
- The conjecture and some of its applications (2012) (0)
- On the number of antipodal bicolored necklaces (2011) (0)
- N T ] 2 4 N ov 2 01 5 On a divisibility relation for Lucas sequences (2018) (0)
- $$k-$$Fibonacci powers as sums of powers of some fixed primes (2021) (0)
- On Rough and Smooth Neighbors (2007) (0)
- How Smooth Is $\phi(2^n+3)$? (2004) (0)
- Connections of Fermat Numbers with Pascal’s Triangle (2002) (0)
- The Hardy-Ramanujan and Landau theorems (2012) (0)
- On the Diophantine equation f(n)=u!+v!, (2013) (0)
- Primes and composites in the determinant Hosoya triangle (2022) (0)
- On the Euler Function of Y-Coordinates of Pell Equations and Repdigits (2022) (0)
- On the number of polynomial maps into Z_n (2006) (0)
- Powerful values of quadratic polynomials. (2011) (0)
- Counting the number of economical numbers (2006) (0)
- $L$-FUNCTIONS OF ELLIPTIC CURVES AND BINARY RECURRENCES (2013) (0)
- ON A SERIES INVOLVING 5(1) ·5(2) ... ·5(n) (2006) (0)
- Setting the stage for the proof of the prime number theorem (2012) (0)
- On Positive Integers n with a Certain (2009) (0)
- X-coordinates of Pell Equations in Various Sequences (2021) (0)
- Equations Involving Arithmetic Functions of Factorials Ecuaciones (2000) (0)
- On an arithmetic function considered by Pillai par (2010) (0)
- 9 S ep 2 00 1 Products of Factorials Modulo p (2003) (0)
- On integers which are the sum of a power of 2 and a polynomial value (2014) (0)
- On the difference of arithmetic functions at consecutive arguments (2008) (0)
- Romanov type problems (2018) (0)
- Polynomial values of sums of products of consecutive integers (2017) (0)
- On Petersson’s partition limit formula (2020) (0)
- Power of Two{Classes in k{Generalized (2014) (0)
- Counting permutation equivalent degree six binary polynomials invariant under the cyclic group (2016) (0)
- On Fibonacci numbers which are elliptic Carmichael (2016) (0)
- Carmichael numbers in the sequence (k2^n+1)_{n\ge 1} (2013) (0)
- Skolem’s conjecture confirmed for a family of exponential equations, II (2021) (0)
- ON A CONJECTURE OF ERDÖS AND GRAHAM 289 (2007) (0)
- The Number Of Permutations Which Form Arithmetic Progressions Modulo m (2014) (0)
- On consecutive integers divisible by the number of their divisors (2016) (0)
- THE DIOPHANTINE EQUATION (cid:80) kj =1 jf pj = l qn (2022) (0)
- ACKNOWLEDGMENT OF PRIORITY: "ON SOME PROBLEMS OF MÅKOWSKI-SCHINZEL AND ERDéS CONCERNING THE ARITHMETICAL FUNCTIONS AND " (2012) (0)
- The global behavior of arithmetic functions (2012) (0)
- Noncototients and Nonaliquots (2004) (0)
- There are no Diophantine quadruples of Fibonacci numbers (2018) (0)
- On Numbers of the Form P + 2 (2014) (0)
- Erratum to: On the length of arithmetic progressions in linear combinations of S-units (2014) (0)
- On prime factors of the sum of two k-Fibonacci numbers (2017) (0)
- ON THE DIFFERENCE OF VALUES OF THE KERNEL FUNCTION AT CONSECUTIVE INTEGERS (2003) (0)
- On a Diophantine equation of Ayad and Kihel (2012) (0)
- 151-Character sums and products of factorials modulo p par MOUBARIZ (0)
- On the largest prime factor of the partition function of n (2012) (0)
- 107 Average order in cyclic groups par (0)
- Multiplicative Diophantine equations with factors from different Lucas sequences (2017) (0)
- The Maximum of the Degree ofNonholonomy for the Car withn TrailersFlorian (1994) (0)
- The Maximum of the Degree ofNonholonomy for the Car withn TrailersFlorian (1994) (0)
- Solutions to even-numbered problems (2012) (0)
- Repdigits in k-Lucas sequences (2014) (0)
- Small Fields with Large Class Groups (2020) (0)
- Power values of the product of the Euler function and the sum of divisors function (2015) (0)
- Primality of Fermat Numbers (2002) (0)
- On the First Digits of the Fibonacci Numbers and Their Euler Function (2014) (0)
- On the Period mod m of Polynomially-Recursive Sequences: a Case Study (2019) (0)
- On the erratic behavior of the Ramanujan \tau-function in short intervals (2017) (0)
- Erratic behavior of Fourier-coefficients of modular forms in short intervals (2017) (0)
- Palindromes in linear recurrence sequences (2013) (0)
- Products of Fibonacci numbers with indices in an interval and at most four omitted being a power (2009) (0)
- Irrationality of Power Series for Various Number (2005) (0)
- An inequality between prime powers dividing n (2002) (0)
- Linear independence results for the values of divisor functions series (Analytic Number Theory and Related Areas) (2018) (0)
- On Pillai’s problem with the Fibonacci and Pell sequences (2018) (0)
- Positive Integers n Such That σ(φ(n)) = σ(n) (2008) (0)
- On the Exponential Diophantine Equation $F_{n+1}^x - F_{n-1}^x = F_m^y$ (2022) (0)
- N ov 2 01 6 Collinear CM-points (2016) (0)
- A note on the Ramanujan--Nagell equation (2004) (0)
- SOME REMARKS ON A RESULT OF F. LUCA AND I. SHPARLINSKI (2011) (0)
- Unbounded Integer Sequences (A n ) n≥0 with A n+1A n−1− A n 2 Bounded are of Fibonacci Type (2001) (0)
- Diophantine equations with products of consecutive members of binary recurrences (2018) (0)
- On an exponential Diophantine equation involving powers of consecutive terms of the Padovan sequence (2022) (0)
- Repdigits as sums of four Pell numbers (2018) (0)
- A ug 2 01 9 Trinomials with given roots (2019) (0)
- On the transcendence of a series related to Sturmian words (2022) (0)
- Algebraic independence results for the infinite products generated by Fibonacci numbers (2013) (0)
- Products of factorials in Smarandache type expressions (abstract) (1997) (0)
- Fundamentals of Number Theory (2002) (0)
- SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n! (2008) (0)
- Counting terms Un of third order linear recurrences with Un = u2 + nv2 (2017) (0)
- Trinomials with integral S-unit coefficients having a quadratic factor (2017) (0)

This paper list is powered by the following services:

## Other Resources About Florian Luca

## What Schools Are Affiliated With Florian Luca?

Florian Luca is affiliated with the following schools: