List of number theory 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
• Rational number
  • Dyadic fraction
  • Recurring decimal
  • Farey sequence
    • Ford circle

Modular arithmetic

• Linear congruence theorem
• Method of successive substitution
• 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

Primality tests and factorization

• 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
• AKS primality test
• Integer factorization
  • Lenstra elliptic curve factorization
  • General number field sieve
  • Shor's algorithm

Arithmetic functions

• 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

Analytic number theory: additive problems

• 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

Algebraic number theory

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

Quadratic forms

L-functions

• Riemann zeta function
• Dirichlet series
• Euler product
• Prime number theorem
  • Offset logarithmic integral
  • Legendre's constant
  • 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
  • Mertens function, Mertens conjecture, Meissel-Mertens constant
• 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

Diophantine equations

• 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

Diophantine approximation

• 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)
• Beatty's theorem
• Geometry of numbers
  • Minkowski's theorem
  • Pick's theorem
• Effective results in number theory
• Mahler's theorem

Named primes

• Cullen prime
• Fermat prime
• Mersenne prime
  • Great Internet Mersenne Prime Search
• Newman-Shanks-Williams prime
• Wall-Sun-Sun prime
• Wieferich prime
• Wilson prime
• Wolstenholme prime
• Woodall prime
• Prime pages

Pseudo-random numbers

• 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

Recreational topics

NB Listing here is not pejorative, 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
• Triangular square number
• Smith numbers
• Semiprime
• Almost prime
• Unique prime
• Factorial prime
• Permutable prime
• Ulam spiral
• Magic square
  • Prime reciprocal magic square
• Magic cube
  • Perfect magic cube
  • Semiperfect magic cube
  • Bimagic cube
  • Multimagic cube
• Magic tesseract
• Squaring the square
• Polydivisible number

Referenced By