# ⓘ List of number theory topics

## ⓘ List of number theory topics

• Highly composite number
• Composite number
• Parity
• Even and odd numbers
• Least common multiple
• Extended Euclidean algorithm
• Divisor, aliquot part
• Greatest common divisor
• Coprime
• Euclids lemma
• Table of divisors
• Bezouts identity, Bezouts lemma
• Euclidean algorithm
• Prime number, prime power
• Bonses inequality
• Prime factor
• Table of prime factors
• Formula for primes
• Factorization
• RSA number
• Square-free integer
• Square-free polynomial
• Fundamental theorem of arithmetic
• Square-free
• Power of two
• Integer-valued polynomial
• Square number

## 1. Fractions

• Farey sequence
• Cyclic number
• Ford circle
• Irreducible fraction = in lowest terms
• Unit fraction
• Stern–Brocot tree
• Rational number
• Recurring decimal
• Dedekind sum
• Egyptian fraction

## 2. Modular arithmetic

• Montgomery reduction
• Modular exponentiation
• Fermats little theorem
• Method of successive substitution
• Proofs of Fermats little theorem
• Linear congruence theorem
• Chinese remainder theorem
• Eulers totient function
• Nontotient
• Noncototient
• Fermat quotient
• Eulers theorem
• Multiplicative order
• Discrete logarithm
• Wilsons theorem
• Primitive root modulo n
• Gausss lemma number theory
• Eulers criterion
• Legendre symbol
• Congruence of squares
• Mod n cryptanalysis
• Luhn formula

## 3. Arithmetic functions

• Mobius function
• Erdos–Kac theorem
• Multiplicative function
• Mobius inversion formula
• Dirichlet convolution
• Landaus function
• Bell numbers
• Pentagonal number theorem
• Divisor function
• Partition function number theory
• Integer partition
• Liouville function
• Bell series
• Lambert series

## 4. Analytic number theory: additive problems

• Twin prime
• Bruns constant
• Goldbachs conjecture
• Cousin prime
• Sexy prime
• Goldbachs weak conjecture
• Prime triplet
• Cunningham chain
• Sophie Germain prime
• Bateman–Horn conjecture
• Brahmagupta–Fibonacci identity
• Eulers four-square identity
• Warings problem
• Lagranges four-square theorem
• Hardy–Littlewood circle method
• Second Hardy–Littlewood conjecture
• Schinzels hypothesis H
• Taxicab number
• Generalized taxicab number
• Sierpinski number
• Schnirelmann density
• Sumset
• Landau–Ramanujan constant
• Seventeen or Bust
• Cabtaxi number
• Nivens constant

## 5. L-functions

• Hurwitz zeta function
• Basel problem on ζ2
• Riemann zeta function
• Agoh–Giuga conjecture
• Von Staudt–Clausen theorem
• Bernoulli number
• Dirichlet series
• Prime-counting function
• Prime number theorem
• Euler product
• Meissel–Lehmer algorithm
• Legendres constant
• Bertrands postulate
• Offset logarithmic integral
• Proof of Bertrands postulate
• Skewes number
• Proof that the sum of the reciprocals of the primes diverges
• Cramers conjecture
• Riemann hypothesis
• De Bruijn–Newman constant
• Generalized Riemann hypothesis
• Critical line theorem
• Hilbert–Polya conjecture
• Mertens function, Mertens conjecture, Meissel–Mertens constant
• Dirichlet L-series
• Siegel zero
• Dirichlet character
• Elliott–Halberstam conjecture
• Dirichlets theorem on arithmetic progressions
• Linniks theorem
• Local zeta function
• Weil conjectures
• Functional equation L-function
• Chebotarevs density theorem
• Cusp form
• Hecke operator
• modular group
• Modular curve
• Eisenstein series
• Modular form
• Congruence subgroup
• Selberg trace formula
• Birch and Swinnerton-Dyer conjecture
• Automorphic form
• modularity theorem
• Artin conjecture
• Sato–Tate conjecture
• Langlands program

## 6. Diophantine equations

• Elliptic curve
• Pythagorean triple
• Arithmetic of abelian varieties
• Congruent number
• Pells equation
• Mazurs torsion theorem
• Mordell–Weil theorem
• Mordell curve
• Elliptic divisibility sequences
• Nagell–Lutz theorem
• Mordell conjecture
• Eulers sum of powers conjecture
• Fermats Last Theorem
• Matiyasevichs theorem
• Catalans conjecture
• abc Conjecture
• Hasse principle
• Diophantine set
• Pillais conjecture
• Hundred Fowls Problem
• 1729

## 7. Diophantine approximation

• Integer square root
• Irrational number
• Square root of two
• Algebraic number
• Salem number
• Davenport–Schmidt theorem
• Pisot–Vijayaraghavan number
• Hilberts seventh problem
• Lindemann–Weierstrass theorem
• e mathematical constant
• Transcendental number
• Proof that e is irrational
• pi, list of topics related to pi
• Squaring the circle
• Gelfond–Schneider theorem
• Erdos–Borwein constant
• Generalized continued fraction
• Khinchins constant
• Continued fraction
• Liouville number
• Mathematical constant sorted by continued fraction representation
• Gauss–Kuzmin–Wirsing operator
• Lochs theorem
• Minkowskis question mark function
• Levys constant
• Gelfond–Schneider constant
• Thue–Siegel–Roth theorem
• Equidistribution mod 1
• Beattys theorem
• Kroneckers theorem
• Littlewood conjecture
• Illustration of a low-discrepancy sequence
• Constructions of low-discrepancy sequences
• Prouhet–Thue–Morse constant
• Discrepancy function
• Halton sequences
• Low-discrepancy sequence
• Picks theorem
• Minkowskis theorem
• Mahlers compactness theorem
• Geometry of numbers
• Effective results in number theory
• Mahlers theorem
• Mahler measure

## 8. Sieve methods

• Sieve of Atkin
• Larger sieve
• Function field sieve
• Turan sieve
• General number field sieve
• Sieve of Sundaram
• Large sieve
• Brun sieve
• Selberg sieve
• Sieve of Eratosthenes

## 9. Named primes

• Mersenne prime
• New Mersenne conjecture
• Chen prime
• Cullen prime
• Fermat prime
• Great Internet Mersenne Prime Search
• Sophie Germain prime, safe prime
• Wieferich prime
• Wilson prime
• Woodall prime
• Prime pages
• Wagstaff prime
• Newman–Shanks–Williams prime
• Wolstenholme prime
• Primorial prime
• Wall–Sun–Sun prime

## 10. Combinatorial number theory

• Polynomial method
• Covering system
• Van der Waerdens theorem
• Szemeredis theorem
• Erdos–Ginzburg–Ziv theorem
• Erdos–Graham conjecture
• Gilbreaths conjecture
• Collatz conjecture
• Znams problem
• Small set combinatorics

### 11.1. Computational number theory Primality tests

• Probabilistic algorithm
• Euler pseudoprime
• Probable prime
• Trial division
• Fermat primality test
• Carmichael number
• Prime factorization algorithm
• Pseudoprime
• Fibonacci pseudoprime
• Sieve of Eratosthenes
• Euler–Jacobi pseudoprime
• Miller–Rabin primality test
• NewPGen
• Baillie-PSW primality test
• Lucas–Lehmer primality test
• AKS primality test
• Lucas–Lehmer test for Mersenne numbers

### 11.2. Computational number theory Integer factorization

• General number field sieve
• Pollards p − 1 algorithm
• Special number field sieve
• RSA Factoring Challenge
• Pollards rho algorithm
• Shors algorithm
• Lenstra elliptic curve factorization

### 11.3. Computational number theory Pseudo-random numbers

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

## 12. Arithmetic dynamics

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

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