# List of number theory topics

Updated on

## Contents

• 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
• ## Fractions

• Rational number
• Unit fraction
• Irreducible fraction = in lowest terms
• 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
• Euler's criterion
• Legendre symbol
• Gauss's lemma (number theory)
• Congruence of squares
• Luhn formula
• Mod n cryptanalysis
• ## Arithmetic functions

• Multiplicative 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
• 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

• 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
• 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
• 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
• 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
• ## 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
• 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
• ## References

List of number theory topics Wikipedia

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