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
- Prime factor
- Formula for primes
- Factorization
- Fundamental theorem of arithmetic
- Square-free
- Perfect square
- Power of two
- Integer-valued polynomial
Fractions
- Rational number
- Unit fraction
- Irreducible fraction = in lowest terms
- Dyadic fraction
- Recurring decimal
- Farey sequence
- Ford circle
- Stern-Brocot tree
- Egyptian fraction
Modular arithmetic
- Montgomery reduction
- Modular exponentiation
- 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
- Congruence of squares
- Luhn formula
- Mod n cryptanalysis
Primality tests and factorization
Main articles:Computational number theory, algorithmic number theory
- Trial division
- Sieve of Eratosthenes
- Primality test
- Fermat primality test
- Miller-Rabin primality test
- Lucas-Lehmer primality test
- Lucas-Lehmer test for Mersenne primes
- AKS primality test
- NewPGen
- Integer factorization, prime factorization algorithm
- RSA Factoring Challenge
Arithmetic functions
- Multiplicative function
- Additive function
- Dirichlet convolution
- Möbius function
- Sigma function
- Divisor function
- Liouville function
- Partition function (number theory)
Analytic number theory: additive problems
- Twin prime
- Cousin prime
- Prime quadruplet
- Sexy prime
- Sophie Germain prime
- Cunningham chain
- Goldbach's conjecture
- Second Hardy-Littlewood conjecture
- Schinzel's hypothesis H
- Waring's problem
- Cabtaxi number
- Schnirelmann density
- Sumset
- Landau-Ramanujan constant
- Sierpinski number
Algebraic number theory
See list of algebraic number theory topics
Quadratic forms
L-functions
- Riemann zeta function
- Basel problem on ζ(2)
- Hurwitz zeta function
- Dirichlet series
- Euler product
- Prime number theorem
- Riemann hypothesis
- Dirichlet character
- Dirichlet L-series
- Dirichlet's theorem
- 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
- Taniyama-Shimura theorem
Diophantine equations
- Pythagorean triple
- Pell's equation
- Elliptic curve
- Fermat's last theorem
- Mordell conjecture
- Euler's conjecture
- abc Conjecture
- Catalan's conjecture
- Pillai's conjecture
- Hasse principle
- Diophantine set
- Matiyasevich's theorem
- One thousand seven hundred and twenty nine
Diophantine approximation
- Irrational number
- Liouville number
- Continued fraction
- Kronecker's theorem
- Thue-Siegel-Roth theorem
- Prouhet-Thue-Morse constant
- Gelfond-Schneider constant
- Beatty's theorem
- Littlewood conjecture
- Discrepancy function
- Geometry of numbers
- Effective results in number theory
- Mahler's theorem
Sieve methods
Named primes
- Cullen prime
- Euler prime
- Fermat prime
- Mersenne prime
- Newman-Shanks-Williams prime
- Wagstaff prime
- Wall-Sun-Sun prime
- Wieferich prime
- Wilson prime
- Wolstenholme prime
- Woodall prime
- Prime pages
Pseudo-random numbers
- Pseudorandom number generator
- Middle-square method
- Blum Blum Shub
- ISAAC
- Lagged Fibonacci generator
- Linear congruential generator
- Linear feedback shift register
- Shrinking generator
- Stream cipher
History
- Disquisitiones Arithmeticae
- On the Number of Primes Less Than a Given Magnitude
- Vorlesungen über Zahlentheorie
Recreational topics
NB Listing here is not pejorative, 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
- Lucas sequence
- Digital sum
- Persistence of a number
- Normal number
Number sequences
- Figurate numbers
- Polygonal number
- Pentagonal number
- Hexagonal number
- Heptagonal number
- Octagonal number
- Nonagonal number
- Decagonal number
- Centered square number
- Centred pentagonal number
- Centered hexagonal number
- Tetrahedral number
- Pyramidal number
- Octahedral number
- Star number
- Perfect number
- Amicable number
- Sociable number
- Abundant number
- Deficient number
- Aliquot sequence
- Super-Poulet number
- Lucky number
- Happy number
- Unhappy number
- Powerful number
- Primeval number
- Repunit
- Repdigit
- Palindromic number
- Automorphic number
- Triangular square number
- Smith numbers
- Polydivisible number
- Harmonic divisor number
- Sphenic number
- Keith number
- Kaprekar number
- Smith number
- Harshad number
- Double Mersenne number
- Zeisel number
- Heteromecic number
- Niven numbers
- Superparticular number
- Untouchable number
- Self number
- Highly totient number
Prime and related sequences
- Semiprime
- Almost prime
- Unique prime
- Factorial prime
- Permutable prime
- Palindromic prime
- Cuban prime
- Lucky prime
Magic squares, etc.
- Ulam spiral
- Magic star
- Magic square
- Magic cube
- Magic tesseract
- Perfect magic tesseract
- Semiperfect magic tesseract
- Magic hypercube
- Magic constant
- Squaring the square
de:Liste zahlentheoretischer Artikel fr:Liste des matičres de la théorie des nombres