User:Redgolpe/Number theory

Number theory

• Euler's totient function
• Goldbach conjecture
• Jacobi symbol
• Legendre symbol
• Quadratic reciprocity
• Quadratic residue
• Riemann hypothesis

Group theory

• Group (mathematics)
• Abelian group
• Field (mathematics)
• Ring (algebra)

Prime number

• Fundamental theorem of arithmetic
• Mertens' theorems
• Mersenne prime

Primality test

• Fermat primality test (1640)
• Wilson's theorem (1773)
• Pocklington primality test (1914)
• Miller–Rabin primality test (1975)
• Solovay–Strassen primality test (1977)

Integer factorization

• Sieve of Eratosthenes
• Fermat's factorization method
• Euler's factorization method
• Dixon's factorization method
• Continued fraction factorization
• Quadratic sieve
• General number field sieve
• Special number field sieve
• Shor's algorithm

Algebraic-group factorization algorithm

• Pollard's p - 1 algorithm
• Lenstra elliptic curve factorization

External links

Lists

Primes

• The 20 largest primes of various forms
• The 5000 largest known primes
• Non-trivial gigantic primes
• Prime constellation records
• Prime generalized repunits
• Proth search page
• The top-20 prime gaps

Probable primes

• Henri & Renaud Lifchitz's PRP Top records

Factorizations

• Factorization of partition numbers
• Fibonacci and Lucas factorizations
• Factorizations of cyclotomic numbers

Papers

• Jack Chernick: On Fermat's simple theorem (1939)
• D.E. Daykin and L.A.G. Dresel: Factorization of Fibonacci numbers (1970)
• Arjen Klaas Lenstra, Hendrik Willem Lenstra, Jr. and L. Lováasz: Factoring polynomials with rational coefficients, contains the LLL algorithm (1982)
• John Brillhart, Peter L. Montgomery and Robert D. Silverman: Tables of Fibonacci and Lucas factorizations (1988)
• A.O.L. Atkin and F. Morain: "Elliptic curves and primality proving" (1992) CiteSeer^x: 10.1.1.30.8758
• Arne Storjohann: "Faster algorithms for integer lattice basis reduction" (1996) CiteSeer^x: 10.1.1.52.6484
• John Brillhart: Note on Fibonacci primality testing (1997)
• Sergei V. Konyagin and Carl Pomerance: On primes recognizable in deterministic polynomial time (1997)
• Harvey Dubner and Wilfrid Keller: New Fibonacci and Lucas primes (1999)
• Chris K. Caldwell: An amazing prime heuristic (2000)
• John H. Jaroma: Factoring generalized repunits (2007)
• Don Coppersmith, Nick Howgrave-Graham and S.V. Nagaraj: Divisors in residue classes, constructively (2007)
• Chris Monico: GGNFS documentation (2007)
• Jeff Gilchrist: Beginners Guide to NFS factoring using GGNFS and MSIEVE (updated 2010)