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=

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 &amp; 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)
 * Arne Storjohann: "Faster algorithms for integer lattice basis reduction" (1996)
 * 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)