List of number theory topics
This is a list of number theory topics, by Wikipedia page. See also list of cryptology topics.
Factors
- Composite number
- Even and odd numbers
- Divisor
- Prime number
- Factorization
- Fundamental theorem of arithmetic
- Square-free
- Perfect square
- Dyadic fraction
- Farey sequence
Modular arithmetic
- Linear congruence theorem
- Method of successive substitution
- Chinese remainder theorem
- Fermat's little theorem
- Euler's totient function
- Euler's theorem
- Wilson's theorem
- Primitive root modulo n
- Quadratic residue
- Luhn formula
Primality tests and factorization
- Sieve of Eratosthenes
- Primality test
- Fermat primality test
- Miller-Rabin primality test
- Lucas-Lehmer primality test
- AKS primality test
- Integer factorization
Arithmetic functions
- Multiplicative function
- Additive function
- Dirichlet convolution
- Möbius function
- Sigma function
- Liouville function
- Partition function (number theory)
Analytic number theory: additive problems
- Twin prime
- Cousin prime
- Sexy prime
- Sophie Germain prime
- Cunningham chain
- Goldbach's conjecture
- Waring's problem
- Schnirelmann density
Algebraic number theory
- Gaussian integer, Gaussian rational
- Algebraic number field
- Global field
- Ideal class group
- Root of unity
- Abelian extension
- Quadratic reciprocity
- Class field theory
- Totally real field
- P-adic number
- Local field
- Adele ring
- Iwasawa theory
Quadratic forms
L-functions
- Riemann zeta function
- Dirichlet series
- Euler product
- Prime number theorem
- Riemann hypothesis
- Dirichlet character
- Dirichlet L-series
- Dirichlet's theorem
- Local zeta function
- Modular form
- Langlands program
- Taniyama-Shimura theorem
Diophantine equations
- Pythagorean triple
- Pell's equation
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Diophantine set
- One thousand seven hundred and twenty nine
Diophantine approximation
- Irrational number
- Liouville number
- Liouville constant
- Continued fraction
- Beatty's theorem
- Geometry of numbers
- Effective results in number theory
- Mahler's theorem
Named primes
- Cullen prime
- Fermat prime
- Mersenne prime
- Newman-Shanks-Williams prime
- Wall-Sun-Sun prime
- Wieferich prime
- Wilson prime
- Wolstenholme prime
- Woodall prime
Pseudo-random numbers
- Pseudorandom number generator
- Blum Blum Shub
- ISAAC
- Lagged Fibonacci generator
- Linear congruential generator
- Linear feedback shift register
- Shrinking generator
- Stream cipher
Recreational topics
NB Listing here is not perjorative, since many famous topics in number theory have origins in challenging problems posed purely for their own sake. See recreational mathematics.
- Integer sequence
- Fibonacci sequence
- Figurate numbers
- Polygonal number
- Normal number
- Perfect number
- Amicable number
- Sociable number
- Abundant number
- Deficient number
- Super-Poulet number
- Lucky number
- Repunit
- Repdigit
- Palindromic number
- Automorphic number
- Triangular square number
- Smith numbers
- Semiprime
- Almost prime
- Unique prime
- Factorial prime
- Permutable prime
- Ulam spiral
- Magic square
- Magic cube
- Magic tesseract
- Squaring the square
- Polydivisible number
