List of number theory topics
Template:Short description This is a list of topics in number theory. See also:
Divisibility
- Composite number
- Even and odd numbers
- Divisor, aliquot part
- Prime number, prime power
- Prime factor
- Formula for primes
- Factorization
- Fundamental theorem of arithmetic
- Square-free
- Square number
- Power of two
- Integer-valued polynomial
Fractions
- Rational number
- Unit fraction
- Irreducible fraction = in lowest terms
- Dyadic fraction
- Recurring decimal
- Cyclic number
- Farey sequence
- Dedekind sum
- Egyptian fraction
Modular arithmetic
- Montgomery reduction
- Modular exponentiation
- Linear congruence theorem
- Method of successive substitution
- Chinese remainder theorem
- Fermat's little theorem
- Fermat quotient
- Euler's totient function
- Euler's theorem
- Wilson's theorem
- Primitive root modulo n
- Quadratic residue
- Congruence of squares
- Luhn formula
- Mod n cryptanalysis
Arithmetic functions
- Multiplicative function
- Additive function
- Dirichlet convolution
- Erdős–Kac theorem
- Möbius function
- Divisor function
- Liouville function
- Partition function (number theory)
- Bell series
- Lambert series
Analytic number theory: additive problems
- Twin prime
- Cousin prime
- Prime triplet
- Prime quadruplet
- Sexy prime
- Sophie Germain prime
- Cunningham chain
- Goldbach's conjecture
- Second Hardy–Littlewood conjecture
- Hardy–Littlewood circle method
- Schinzel's hypothesis H
- Bateman–Horn conjecture
- Waring's problem
- Cabtaxi number
- Schnirelmann density
- Sumset
- Landau–Ramanujan constant
- Sierpinski number
- Niven's constant
Algebraic number theory
See list of algebraic number theory topics
Quadratic forms
L-functions
- Riemann zeta function
- Dirichlet series
- Euler product
- Prime number theorem
- Riemann hypothesis
- Dirichlet character
- Dirichlet L-series
- Dirichlet's theorem on arithmetic progressions
- Functional equation (L-function)
- Chebotarev's density theorem
- Local zeta function
- Modular form
- 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
- 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
- Liouville number
- Irrationality measure
- Simple 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
- Geometry of numbers
- 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
- 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
- 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 tests
- Prime factorization algorithm
- Trial division
- Sieve of Eratosthenes
- Probabilistic algorithm
- Fermat primality test
- 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 numbers
- Pseudorandom 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
see also List of random number generators.
Arithmetic dynamics
- Aliquot sequence and Aliquot sum dynamics
- Collatz conjecture
- Digit sum dynamics
- Digit product dynamics
- Lychrel number
- Perfect digital invariant