List of number theory topics

• List of recreational number theory topics
• Topics in cryptography

  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

  Fraction">Fraction (mathematics)">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
• Congruence of squares
• Luhn formula
• Mod n cryptanalysis

  [Arithmetic function]s

• Multiplicative function
• Additive function
• Dirichlet convolution
• Erdős–Kac theorem
• Möbius function
• *Möbius inversion formula
• Divisor function
• Liouville function
• Partition function
• *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]

[Quadratic form]s

• Unimodular lattice
• Fermat's theorem on sums of two squares
• *Proofs of Fermat's theorem on sums of two squares

  [L-function]s

• Riemann zeta function
• *Basel problem on ζ
• *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
• 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 equation]s

• 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
• **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
• *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">Sieve theory">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
• 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]

• Residue number system
• Cunningham project
• Quadratic residuosity problem

  [Primality test]s

• 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 number]s

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

[Arithmetic dynamics]

• Aliquot sequence and Aliquot sum dynamics
• *Abundant number
• *Almost perfect number
• *Amicable number
• *Betrothed numbers
• *Deficient number
• *Quasiperfect number
• *Perfect number
• *Sociable number
• Collatz conjecture
• Digit sum dynamics
• *Additive persistence
• *Digital root
• Digit product dynamics
• *Multiplicative digital root
• *Multiplicative persistence
• Lychrel number
• Perfect digital invariant
• *Happy number

  History

• Disquisitiones Arithmeticae
• "On the Number of Primes Less Than a Given Magnitude"
• Vorlesungen über Zahlentheorie
• Prime Obsession