List of number theory topics

Factors

Composite number

Highly composite number

Even and odd numbers

Parity

Divisor, aliquot part

Greatest common divisor

Least common multiple

Euclidean algorithm

Coprime

Euclid's lemma

Bézout's identity, Bézout's lemma

Extended Euclidean algorithm

Table of divisors

Prime number, prime power

Bonse's inequality

Prime factor

Table of prime factors

Formula for primes

Factorization

RSA number

Fundamental theorem of arithmetic

Square-free

Square-free integer

Square-free polynomial

Square number

Power of two

Integer-valued polynomial

Fractions

Rational number

Unit fraction

Irreducible fraction = in lowest terms

Dyadic fraction

Recurring decimal

Cyclic number

Farey sequence

Ford circle

Stern–Brocot tree

Dedekind sum

Egyptian fraction

Modular arithmetic

Montgomery reduction

Modular exponentiation

Linear congruence theorem

Method of successive substitution

Chinese remainder theorem

Fermat's little theorem

Proofs of Fermat's little theorem

Fermat quotient

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's lemma (number theory)

Congruence of squares

Luhn formula

Mod n cryptanalysis

Arithmetic functions

Multiplicative function

Additive function

Dirichlet convolution

Erdős–Kac theorem

Möbius function

Möbius inversion formula

Divisor function

Liouville function

Partition function (number theory)

Integer partition

Bell numbers

Landau's function

Pentagonal number theorem

Bell series

Lambert series

Analytic number theory: additive problems

Twin prime

Brun's constant

Cousin prime

Prime triplet

Prime quadruplet

Sexy prime

Sophie Germain prime

Cunningham chain

Goldbach's conjecture

Goldbach's weak conjecture

Second Hardy–Littlewood conjecture

Hardy–Littlewood circle method

Schinzel's hypothesis H

Bateman–Horn conjecture

Waring's problem

Brahmagupta–Fibonacci identity

Euler's four-square identity

Lagrange's four-square theorem

Taxicab number

Generalized taxicab number

Cabtaxi number

Schnirelmann density

Sumset

Landau–Ramanujan constant

Sierpinski number

Seventeen or Bust

Niven's constant

Algebraic number theory

See list of algebraic number theory topics

Quadratic forms

Unimodular lattice

Fermat's theorem on sums of two squares

Proofs of Fermat's theorem on sums of two squares

L-functions

Riemann zeta function

Basel problem on ζ(2)

Hurwitz zeta function

Bernoulli number

Agoh–Giuga conjecture

Von Staudt–Clausen theorem

Dirichlet series

Euler product

Prime number theorem

Prime-counting function

Meissel–Lehmer algorithm

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

Critical line theorem

Hilbert–Pólya conjecture

Generalized Riemann hypothesis

Mertens function, Mertens conjecture, Meissel–Mertens constant

De Bruijn–Newman constant

Dirichlet character

Dirichlet L-series

Siegel zero

Dirichlet's theorem on arithmetic progressions

Linnik's theorem

Elliott–Halberstam conjecture

Functional equation (L-function)

Chebotarev's density theorem

Local zeta function

Weil conjectures

Modular form

modular group

Congruence subgroup

Hecke operator

Cusp form

Eisenstein series

Modular curve

Ramanujan–Petersson conjecture

Birch and Swinnerton-Dyer conjecture

Automorphic form

Selberg trace formula

Artin conjecture

Sato–Tate conjecture

Langlands program

modularity theorem

Diophantine equations

Pythagorean triple

Pell's equation

Elliptic curve

Nagell–Lutz theorem

Mordell–Weil theorem

Mazur's torsion theorem

Congruent number

Arithmetic of abelian varieties

Elliptic divisibility sequences

Mordell curve

Fermat's Last Theorem

Mordell conjecture

Euler's sum of powers conjecture

abc Conjecture

Catalan's conjecture

Pillai's conjecture

Hasse principle

Diophantine set

Matiyasevich's theorem

Hundred Fowls Problem

1729

Diophantine approximation

Davenport–Schmidt theorem

Irrational number

Square root of two

Quadratic irrational

Integer square root

Algebraic number

Pisot–Vijayaraghavan number

Salem 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

Erdős–Borwein constant

Liouville number

Continued fraction

Mathematical constant (sorted by continued fraction representation)

Khinchin's constant

Lévy's constant

Lochs' theorem

Gauss–Kuzmin–Wirsing operator

Minkowski's question mark function

Generalized continued fraction

Kronecker's theorem

Thue–Siegel–Roth theorem

Prouhet–Thue–Morse constant

Gelfond–Schneider constant

Equidistribution mod 1

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

Mahler measure

Effective results in number theory

Mahler's theorem

Sieve methods

Brun sieve

Function field sieve

General number field sieve

Large sieve

Larger sieve

Quadratic sieve

Selberg sieve

Sieve of Atkin

Sieve of Eratosthenes

Sieve of Sundaram

Turán sieve

Named primes

Chen prime

Cullen prime

Fermat prime

Sophie Germain prime, safe prime

Mersenne prime

New Mersenne conjecture

Great Internet Mersenne Prime Search

Newman–Shanks–Williams prime

Primorial prime

Wagstaff prime

Wall–Sun–Sun prime

Wieferich prime

Wilson prime

Wolstenholme prime

Woodall prime

Prime pages

Combinatorial number theory

Covering system

Small set (combinatorics)

Erdős–Ginzburg–Ziv theorem

Polynomial method

Van der Waerden's theorem

Szemerédi's theorem

Collatz conjecture

Gilbreath's conjecture

Erdős–Graham conjecture

Znám's problem

Computational number theory

Note: Computational number theory is also known as algorithmic number theory.

Residue number system

Cunningham project

Quadratic residuosity problem

Primality tests

Prime factorization algorithm

Trial division

Sieve of Eratosthenes

Probabilistic algorithm

Fermat primality test

Pseudoprime

Carmichael number

Euler pseudoprime

Euler–Jacobi pseudoprime

Fibonacci pseudoprime

Probable prime

Baillie-PSW primality test

Miller–Rabin primality test

Lucas–Lehmer primality test

Lucas–Lehmer test for Mersenne numbers

AKS primality test

NewPGen

Integer factorization

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

Pseudo-random numbers

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

History

Disquisitiones Arithmeticae

"On the Number of Primes Less Than a Given Magnitude"

Vorlesungen über Zahlentheorie

Prime Obsession