John Brillhart
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American mathematician
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Mathematics
Why Is John Brillhart Influential?
(Suggest an Edit or Addition)According to Wikipedia, John David Brillhart was a mathematician who worked in number theory at the University of Arizona. Early life and education Brillhart was born on November 13, 1930, in Berkeley, California. He studied at the University of California, Berkeley, where he received his A.B. in 1953, his M.A. in 1966, and his Ph.D. in 1967. His doctoral thesis in mathematics was supervised by D. H. Lehmer, with assistance from Leonard Carlitz.
John Brillhart's Published Works
Published Works
- A method of factoring and the factorization of (1975) (224)
- Factorizations of b[n]±1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers (1985) (147)
- On Primitive Trinomials (Mod 2) (1968) (138)
- New primality criteria and factorizations of 2^{}±1 (1975) (138)
- Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial (2004) (59)
- On the Euler and Bernoulli polynomials. (1967) (49)
- Note on the Shapiro polynomials (1970) (41)
- Note on Representing a Prime as a Sum of Two Squares (1972) (40)
- A Case Study in Mathematical Research: The Golay-Rudin-Shapiro Sequence (1996) (37)
- On the Prime Divisors of Polynomials (1971) (36)
- On sums of Rudin-Shapiro coefficients II (1983) (35)
- Some infinite product identities (1988) (33)
- Tables of Fibonacci and Lucas factorizations (1988) (30)
- Some factorizations of 2ⁿ±1 and related results (1967) (28)
- The factorization of $F_7$ (1971) (24)
- Table errata: “New primality criteria and factorizations of 2^{}±1” [Math. Comp. 29 (1975), 620–647; MR 52 #5546] by the author, D. H. Lehmer and J. L. Selfridge (1982) (22)
- Parity results for certain partition functions and identities similar to theta function identities (1987) (22)
- On an Irreducibility Theorem of A. Cohn (1981) (21)
- Cyclotomic properties of the Rudin-Shapiro polynomials. (1976) (19)
- A fundamental modular identity and some applications (1993) (16)
- On the factors of certain Mersenne numbers. II (1960) (16)
- Note on the Single Variable Bell Polynomials (1967) (15)
- On the Rudin-Shapiro polynomials (1973) (13)
- Corrigendum: “Some factorizations of 2ⁿ±1 and related results” (1967) (12)
- Recurring sequences : a collection of papers (1958) (11)
- Bounds for pairs of consecutive seventh and higher power residues (1964) (10)
- Two new factors of Fermat numbers (1975) (10)
- Table errata: Recurring sequences (second edition, Riveon Lematematika, Jerusalem, 1966) by Dov Jarden (1971) (9)
- Some miscellaneous factorizations (1963) (9)
- Factorizations of bn [plus or minus symbol] 1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers (1983) (8)
- On Primitive Trinomials (Mode 2), II (1969) (7)
- Note on irreducibility testing (1980) (5)
- On a certain (mod 2) identity and a method of proof by expansion (1991) (4)
- Concerning the numbers 2^{2}+1, prime (1962) (4)
- Note on the discriminant of certain cyclotomic period polynomials (1992) (3)
- Supplement to Tables of Fibonacci and Lucas Factorizations (1988) (3)
- Table errata: List of prime numbers from 1 to 10,006,721 (reissue, Hafner, New York, 1956) by D. N. Lehmer (1975) (3)
- New Proofs for Two Infinite Product Identities (1992) (3)
- Problems: 10375-10381 (1994) (3)
- Linear quintuple-product identities (2003) (2)
- On the mod 2 reciprocation of infinite modular-part products and the parity of certain partition functions (1990) (2)
- Advanced Problems: 5320-5329 (1965) (2)
- Using Conic Sections to Factor Integers (2016) (2)
- Some modular results on the Euler and Bernoulli polynomials (1972) (2)
- A Note on Euler's Factoring Problem (2009) (2)
- Corrigenda to: “Two new factors of Fermat numbers” (Math. Comp. 29 (1975), 110) (1976) (2)
- Recollections of Leonard Carlitz (including: The publications of Leonard Carlitz) (2012) (1)
- The completion of Euler's factoring formula (2013) (1)
- A Lattice Proof of a Modular Identity (1996) (1)
- A constructive theory of triple and quintuple product identities of the second degree (1998) (1)
- Errata: Dov Jarden, Recurring sequences, second edition, Riveon Lematematika, Jerusalem, 1966 (1972) (1)
- Algorithms for finding and proving balanced Q2 identities (2007) (1)
- V. How to Use the Main Tables (1988) (0)
- Elementary Problems: E1711-E1720 (1964) (0)
- Proving Balanced T 2 and Q 2 Identities Using Modular Forms (2011) (0)
- Erratum to: For 1553-1, read 1053-1 (1980) (0)
- A double inversion formula. (1980) (0)
- II. Convenient Short Tables (1988) (0)
- VI. The Main Tables (1988) (0)
- Elementary Problems: E2968-E2973 (1982) (0)
- New Primality Criteria and Factorizations of 2 TM d = 1 By (2010) (0)
- Factoring work. (1984) (0)
- IV. Update to the Introduction for the Second Edition (1988) (0)
- Update 2.2 to the Second Edition (1988) (0)
- VII. Introduction to the Appendices (1988) (0)
- Factoring Work (1984) (0)
- I. Introduction to the Short Tables (1988) (0)
- III. Introduction to the Main Tables (1988) (0)
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