Florian Luca

Q: What Schools Are Affiliated With Florian Luca

Florian Luca is affiliated with the following schools: University of Ostrava, National Autonomous University of Mexico, Syracuse University, Bielefeld University, University of the Witwatersrand, King Abdulaziz University, University of Alaska Fairbanks, Alexandru Ioan Cuza University, University of Bucharest

Florian Luca's AcademicInfluence.com Rankings

Florian Luca

Mathematics

#946

World Rank

#1647

Historical Rank

Number Theory

#65

World Rank

#95

Historical Rank

Measure Theory

#1342

World Rank

#1689

Historical Rank

mathematics Degrees

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Mathematics

Florian Luca's Degrees

PhD Mathematics University of Bucharest

Why Is Florian Luca Influential?

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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.

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Florian Luca's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

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)
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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)
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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)
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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)
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On Fibonacci Numbers Which Are Elliptic Korselt Numbers (2014) (2)
Number fields in fibers: the geometrically abelian case with rational critical values (2016) (2)
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Nonaliquots and Robbins numbers (2005) (2)
On the error term of a lattice counting problem (2017) (2)
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Fibonacci Numbers with Prime Sums of Complementary Divisors (2014) (2)
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Arithmetic functions monotonic at consecutive arguments (2014) (2)
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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)
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Diophantine triples with values in the sequences of Fibonacci and Lucas numbers (2017) (2)
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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)
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k{generalized Fibonacci numbers of the form (2014) (1)
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Partial Sums of Powers of Prime Factors (2007) (1)
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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)
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Standard Noether normalizations of the graph subring (2006) (1)
Ratios of sums of two Fibonacci numbers equal to powers of 2 (2020) (1)
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Composite positive integers whose sum of prime factors is prime (2020) (1)
Terms of Lucas sequences having a large smooth divisor (2022) (1)
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Prime Divisors Of Some Recurrence Sequence (2007) (1)
Romanov type problems (2018) (1)
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Mackey Functors with Chain Conditions (1998) (1)
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Prime divisors of some shifted products (2005) (1)
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An inequality for Fibonacci numbers (2022) (1)
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Positive integers such that . (2003) (1)
Perfect Pell and Pell–Lucas numbers (2019) (1)
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Diophantine equations involving factorials (2017) (1)
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Quadratic forms representing the $p$-th Fibonacci number (2015) (1)
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Binary recurrences for which powers of two are discriminating moduli (2020) (1)
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The zero-multiplicity of Berstel type sequences (2019) (1)
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Finiteness results for Diophantine triples with repdigit values (2015) (1)
Local Behavior of the Composition of the Aliquot and Co-Totient Functions (2016) (1)
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Minimal Niven numbers (2008) (1)
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The Most Beautiful Theorems on Fermat Numbers (2002) (1)
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Perfect powers in the summatory function of the power tower (2010) (1)
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Power Classes Of Recurrence Sequences (2004) (1)
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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)

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