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 Fractions 3 Modular arithmetic 4 Primality tests and factorization 5 Arithmetic functions 6 Analytic number theory: additive problems 7 Algebraic number theory 8 Quadratic forms 9 L-functions 10 Diophantine equations 11 Diophantine approximation 12 Named primes 13 Pseudo-random numbers 14 History 15 Recreational topics 15.1 Number sequences 15.2 Prime and related sequences 15.3 Magic squares, etc.

Factors

• Composite number
  • Highly composite number
• Even and odd numbers
  • Parity
• Divisor
  • Greatest common divisor
  • Least common multiple
  • Euclidean algorithm
  • Coprime
  • Bézout's identity, Bézout's lemma
  • Extended Euclidean algorithm
  • Table of divisors
• Prime number
• Prime factor
  • Table of prime factors
• Formula for primes
• Factorization
  • RSA number
• Fundamental theorem of arithmetic
• Square-free
• Perfect square
• Power of two
• Integer-valued polynomial

• Rational number
• Unit fraction
• Irreducible fraction = in lowest terms
• Dyadic fraction
• Recurring decimal
• Farey sequence
  • Ford circle
  • Stern-Brocot tree
• Egyptian fraction

• Linear congruence theorem
• Method of successive substitution
• Chinese remainder theorem
• Fermat's little theorem
  • Proofs of Fermat's little theorem
• Euler's totient function
  • Noncototient
  • Nontotient
• Euler's theorem
• Wilson's theorem
• Primitive root modulo n
  • Multiplicative order
  • Discrete logarithm
• Quadratic residue
  • Euler's criterion
  • Legendre symbol
  • Gauss lemma
• Congruence of squares
• Luhn formula
• Mod n cryptanalysis

• Sieve of Eratosthenes
• Primality test
  • Probabilistic algorithm
• Fermat primality test
  • Pseudoprime
  • Carmichael number
  • Euler pseudoprime
  • Euler-Jacobi pseudoprime
  • Fibonacci pseudoprime
  • Probable prime
• Miller-Rabin primality test
• Lucas-Lehmer primality test
• Lucas-Lehmer test for Mersenne primes
• AKS primality test
• NewPGen
• Integer factorization, prime factorization algorithm
  • Pollard's p-1 algorithm
  • Pollard's rho algorithm
  • Lenstra elliptic curve factorization
  • Quadratic sieve
  • Special number field sieve
  • General number field sieve
  • Shor's algorithm
• RSA Factoring Challenge
  • FAFNER

• Multiplicative function
• Additive function
• Dirichlet convolution
• Möbius function
  • Möbius inversion formula
• Sigma function
• Divisor 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
• Second Hardy-Littlewood conjecture
• Schinzel's hypothesis H
• Waring's problem
  • Brahmagupta's identity
  • Euler's four-square identity
  • Lagrange's four-square theorem
  • Taxicab number
  • Generalized taxicab number
• Cabtaxi number
• Schnirelmann density
• Landau-Ramanujan constant
• Sierpinski number
  • Seventeen or bust

• Gaussian integer, Gaussian rational
• Quadratic field
• Algebraic number field
  • Dedekind domain
• Global field
• Ideal class group
  • Stark-Heegner theorem
  • Heegner number
  • Ankeny-Artin-Chowla congruence
• Root of unity
  • Gaussian period, Gauss sum
  • Chowla-Mordell theorem
  • Cyclotomic field
  • Number-theoretic transform
• Dirichlet's unit theorem
• Discriminant
• Ramification
• Abelian extension
• Quadratic reciprocity
• Class field theory
  • Local classfield theory
• Totally real field
• Chowla-Selberg formula
• P-adic number
  • P-adic analysis
  • Local analysis
• Local field
• Adele ring
• Galois module
• Iwasawa theory

L-functions

• Riemann zeta function
  • Basel problem on ζ(2)
  • Hurwitz 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
  • Hilbert-Polya conjecture
  • Generalized Riemann hypothesis
  • Mertens function, Mertens conjecture, Meissel-Mertens constant
  • De Bruijn-Newman constant
• Dirichlet character
• Dirichlet L-series
• Dirichlet's theorem
  • Linnik's theorem
• Functional equation (L-function)
• Chebotarev's density theorem
• Local zeta function
  • Weil conjectures
• Modular form
  • modular group
  • Congruence subgroup
  • Hecke operator
  • Cusp form
  • Modular curve
• Birch and Swinnerton-Dyer conjecture
• Artin conjecture
• Sato-Tate conjecture
• Langlands program
• Taniyama-Shimura theorem

• Pythagorean triple
• Pell's equation
• Elliptic curve
  • Nagell-Lutz theorem
  • Mordell-Weil theorem
  • Arithmetic of abelian varieties
• Fermat's last theorem
• Mordell conjecture
• Euler's conjecture
• abc Conjecture
• Catalan's conjecture
• Pillai's conjecture
• Hasse principle
• Diophantine set
• Matiyasevich's theorem
• One thousand seven hundred and twenty nine

• Irrational number
  • Square root of two
  • Quadratic irrational
  • Algebraic number
    • Pisot-Vijayaraghavan number
  • Transcendental number
    • e (mathematical constant)
    • pi, list of topics related to pi
    • Squaring the circle
    • Proof that e is irrational
    • Lindemann-Weierstrass theorem
    • Hilbert's seventh problem
    • Gelfond-Schneider theorem
  • Erdös-Borwein constant
• Liouville number
• Continued fraction
  • Mathematical constant (sorted by continued fraction representation)
  • Khinchin's constant
  • Generalized continued fraction
• Kronecker's theorem
• Thue-Siegel-Roth theorem
• Beatty's theorem
• Littlewood conjecture
• Discrepancy function
  • Low-discrepancy sequence
  • Illustration of a low-discrepancy sequence
  • Constructions of low-discrepancy sequences
  • Halton sequences
• Geometry of numbers
  • Minkowski's theorem
  • Pick's theorem
  • Mahler's compactness theorem
• Effective results in number theory
• Mahler's theorem

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

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

• Disquisitiones Arithmeticae
• On the Number of Primes Less Than a Given Magnitude
• Vorlesüngen über Zahlentheorie

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
• Lucas sequence
• Digital sum
• Persistence of a number
• Normal number
  • Stoneham number
  • Champernowne constant
  • Absolutely normal number

• Figurate numbers
• Polygonal number
  • Triangular number
  • Square number
• Pentagonal number
• Hexagonal number
• Heptagonal number
• Octagonal number
• Centered square number
• Centred pentagonal number
• Centered hexagonal number
• Tetrahedral number
• Pyramidal number
  • Triangular pyramidal number
  • Square pyramidal number
  • Pentagonal pyramidal number
  • Heptagonal pyramidal number
• Octahedral number
• Star number
• Perfect number
  • Quasiperfect number
  • Almost perfect number
  • Multiply perfect number
  • Hyperperfect number
  • Semiperfect number
  • Primitive semiperfect number
  • Unitary perfect number
  • Weird number
• Amicable number
• Sociable number
• Abundant number
• Deficient number
• Aliquot sequence
• Super-Poulet number
• Lucky number
• Happy number
• Unhappy number
• Powerful number
• Primeval number
• Repunit
  • Repunit (factors)
• Repdigit
• Palindromic number
• Automorphic number
• Triangular square number
• Smith numbers
• Polydivisible number
• Harmonic divisor number
• Sphenic number
• Keith number
• Kaprekar number
• Smith number
• Harshad number
• Double Mersenne number
• Zeisel number
• Heteromecic number

• Semiprime
• Almost prime
• Unique prime
• Factorial prime
• Permutable prime
• Palindromic prime
• Cuban prime
• Lucky prime

• Ulam spiral
• Magic star
• Magic square
  • Frenicle's standard form
  • Prime reciprocal magic square
  • Trimagic square
  • Multimagic square
  • Panmagic square
  • Diabolic square
  • Satanic square
  • Most-perfect square
  • Conway's Lux method for magic squares
• Magic cube
  • Perfect magic cube
  • Semiperfect magic cube
  • Bimagic cube
  • Trimagic cube
  • Multimagic cube
• Magic tesseract
• Perfect magic tesseract
• Semiperfect magic tesseract
• Magic hypercube
• Magic constant
• Squaring the square