List of number theory topics

This is a list of number theory topics, by Wikipedia page. See also list of cryptology topics.

Table of contents

1 Factors 2 Modular arithmetic 3 Primality tests and factorization 4 Arithmetic functions 5 Analytic number theory: additive problems 6 Algebraic number theory 7 Quadratic forms 8 L-functions 9 Diophantine equations 10 Diophantine approximation 11 Named primes 12 Pseudo-random numbers 13 Recreational topics

Factors

• Composite number
  • Highly composite number
• Even and odd numbers
  • Parity
• Divisor
  • Greatest common divisor
  • Least common multiple
  • Euclidean algorithm
  • Coprime
  • Bézout's identity
  • Extended Euclidean algorithm
  • Table of divisors
• Prime number
  • Table of prime factors
• Factorization
  • RSA number
• Fundamental theorem of arithmetic
• Square-free
• Perfect square
• Dyadic fraction
• Farey sequence
  • Ford circle

• Linear congruence theorem
• Chinese remainder theorem
• Fermat's little theorem
  • Proofs of Fermat's little theorem
• Euler's totient function
• Euler's theorem
• Wilson's theorem
• Primitive root modulo n
  • Multiplicative order
  • Discrete logarithm
• Quadratic residue
  • Euler's criterion
  • Legendre symbol
• Luhn formula

• Sieve of Eratosthenes
• Primality test
  • Probabilistic algorithm
• Fermat primality test
  • Pseudoprime
  • Carmichael number
  • Euler pseudoprime
  • Euler-Jacobi pseudoprime
  • Probable prime
• Miller-Rabin primality test
• Lucas-Lehmer primality test
• Integer factorization
  • Lenstra elliptic curve factorization
  • General number field sieve
  • Shor's algorithm

• Multiplicative function
• Additive function
• Dirichlet convolution
• Möbius function
  • Möbius inversion formula
• Sigma function
• Liouville function
• Partition function (number theory)
  • Integer partition
  • Bell numbers
  • Landau's function
  • Pentagonal number theorem

• Twin prime
  • Twin prime conjecture
  • Brun's constant
• Cousin prime
• Sexy prime
• Sophie Germain prime
• Cunningham chain
• Goldbach's conjecture
  • Goldbach's weak conjecture
• Waring's problem
  • Brahmagupta's identity
  • Euler's four-square identity
  • Lagrange's four-square theorem
• Schnirelmann density

• Gaussian integer, Gaussian rational
• Algebraic number field
  • Dedekind domain
• Global field
• Ideal class group
• Root of unity
• Abelian extension
• Quadratic reciprocity
• Class field theory
• Totally real field
• P-adic number
  • P-adic analysis
  • Local analysis
• Local field
• Adele ring
• Iwasawa theory

L-functions

• Riemann zeta function
• Dirichlet series
• Euler product
• Prime number theorem
  • Offset logarithmic integral
  • Skewes' number
  • Bertrand's postulate
    • Proof of Bertrand's postulate
    • Proof that the sum of the reciprocals of the primes diverges
  • Cramér's conjecture
• Riemann hypothesis
  • Generalized Riemann hypothesis
• Dirichlet character
• Dirichlet L-series
• Dirichlet's theorem
  • Linnik's theorem
• Local zeta function
  • Weil conjectures
• Modular form
  • modular group
• Langlands program
• Taniyama-Shimura theorem

• Pythagorean triple
• Pell's equation
• Fermat's last theorem
• Mordell conjecture
• Euler's conjecture
• abc Conjecture
• Diophantine set
• One thousand seven hundred and twenty nine

• Irrational number
  • Square root of two
  • Quadratic irrational
  • Algebraic number
  • Transcendental number
    • e (mathematical constant)
    • pi
    • Squaring the circle
    • Lindemann-Weierstrass theorem
    • Hilbert's sixth problem
  • Erdös-Borwein constant
• Liouville number
  • Liouville constant
• Continued fraction
  • Mathematical constant (sorted by continued fraction representation)
• Geometry of numbers
  • Minkowski's theorem
  • Pick's theorem
• Effective results in number theory

• Cullen prime
• Fermat prime
• Mersenne prime
• Newman-Shanks-Williams prime
• Wall-Sun-Sun prime
• Wieferich prime
• Wilson prime
• Wolstenholme prime
• Woodall prime

• Pseudorandom number generator
  • Pseudorandomness
  • Cryptographically secure pseudo-random number generator
• Blum Blum Shub
• ISAAC
• Lagged Fibonacci generator
• Linear congruential generator
  • Mersenne twister
• Linear feedback shift register
• Shrinking generator
• Stream cipher

NB Listing here is not perjorative, since many famous topics in number theory have origins in challenging problems posed purely for their own sake. See recreational mathematics.

• Integer sequence
• Fibonacci sequence
  • Golden mean base
  • Fibonacci coding
• Figurate numbers
• Polygonal number
  • Triangular number
  • Square number
• Normal number
• Perfect number
  • Quasiperfect number
  • Almost perfect number
  • Multiply perfect number
  • Hyperperfect number
  • Semiperfect number
  • Primitive semiperfect number
  • Weird number
• Amicable number
• Sociable number
• Abundant number
• Deficient number
• Super-Poulet number
• Lucky number
• Repunit
  • Repunit (factors)
• Repdigit
• Palindromic number
• Automorphic number
• Smith numbers
• Semiprime
• Almost prime
• Unique prime
• Ulam spiral
• Magic square
  • Prime reciprocal magic square
• Squaring the square
• Polydivisible number