List of number theory topics
This is a list of topics in number theory. See also:
[Divisibility rule]
- 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
- Successive over-relaxation
- 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 function]s
- 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 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 (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 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 (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
- Irrationality measure
- Simple 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">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 (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.[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
[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