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

list of recreational number theory topics,

list of cryptology topics.

    List of number theory topics
        Factors
        Fraction (mathematics)|Fractions
        Modular arithmetic
        Arithmetic functions
        Analytic number theory: additive problems
        Algebraic number theory
        Quadratic forms
        L-functions
        Diophantine equations
        Diophantine approximation
        Sieve methods
        Named primes
        Combinatorial number theory
        Computational number theory
            Primality tests
            Integer factorization
            Pseudo-random numbers
        History

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Factors

Composite number

Highly composite number

Even and odd numbers

Parity

Divisor, aliquot, aliquant

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

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

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Fraction (mathematics)|Fractions

Rational number

Unit fraction

Irreducible fraction = in lowest terms

Modular arithmetic

Advanced modular arithmetic theory

Montgomery reduction

Modular exponentiation

Linear congruence theorem

Method of successive substitution

Chinese remainder theorem

Fermat's little theorem

Proofs of Fermat's little theorem

Euler's totient function

Primitive root modulo n

Congruence of squares

Luhn formula

Mod n cryptanalysis

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Arithmetic functions

Multiplicative function

Additive function

Dirichlet convolution

Erdős-Kac theorem

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

Bell series

Lambert series

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Analytic number theory: additive problems

Twin prime

Twin prime conjecture

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

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Algebraic number theory
See list of algebraic number theory topics

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Quadratic forms

Unimodular lattice

Fermat's theorem on sums of two squares

Proofs of Fermat's theorem on sums of two squares

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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

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-Polya conjecture

Generalized Riemann hypothesis

Mertens function, Mertens conjecture, Meissel-Mertens constant

De Bruijn-Newman constant

Elliott-Halberstam conjecture

Functional equation (L-function)

Chebotarev's density theorem

Ramanujan-Petersson conjecture

Birch and Swinnerton-Dyer conjecture

Automorphic form

Selberg trace formula

Artin conjecture

Sato-Tate conjecture

Langlands program

Taniyama-Shimura theorem

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Diophantine equations

Mazur's torsion theorem

Congruent number

Arithmetic of abelian varieties

Fermat's last theorem

Matiyasevich's theorem

One thousand seven hundred and twenty nine

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Diophantine approximation

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

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

Mahler's compactness theorem

Mahler measure

Effective results in number theory

Sieve methods

Named primes

Sophie Germain prime, safe prime

Mersenne prime

New Mersenne conjecture

Great Internet Mersenne Prime Search

Newman-Shanks-Williams prime

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

Znám's problem

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Computational number theory

Algorithmic number theory

Residue number system

Cunningham project

Quadratic residuosity problem

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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

Miller-Rabin primality test

Lucas-Lehmer primality test

Lucas-Lehmer test for Mersenne numbers

AKS primality test

NewPGen

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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

FAFNER

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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

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History

Disquisitiones Arithmeticae

On the Number of Primes Less Than a Given Magnitude

Vorlesungen über Zahlentheorie

Prime Obsession

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