Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the questions investigated. See for example the list of number theory topics.

Subcategories

There are 10 subcategories to this category.

Algebraic number theory Analytic number theory C Computational number theory

D Diophantine approximation Diophantine equations I Integer sequences M Modular arithmetic

M cont. Modular forms N Number theoretic algorithms Number theorists

Articles in category "Number theory"

There are 189 articles in this category.

Abc conjecture Abelian variety of CM-type Abundant number Additive function Advanced modular arithmetic theory Agoh-Giuga conjecture Algebraic number Algorithmic number theory Aliquant Aliquot sequence Almost perfect number Almost prime Amenable number Amicable number Ankeny-Artin-Chowla congruence Apéry's theorem Arithmetic function Armstrong number Automorphic form B Basel problem Bateman-Horn conjecture Bell series Bernoulli number Bernoulli polynomials C Cabtaxi number Carmichael number Catalan's conjecture Champernowne constant Character group Chowla-Mordell theorem Chowla-Selberg formula Clock arithmetic Collatz conjecture Colossally abundant number Computational number theory Continued fraction Coprime Cunningham project Cyclic number D Dedekind sum Deficient number Diophantine approximation Dirichlet convolution Dirichlet's theorem on arithmetic progressions Discrepancy function Divisor Divisor function Double Mersenne number Double Mersenne prime E Effective results in number theory Euclid's lemma Euler prime Euler pseudoprime Euler's conjecture Euler's totient function Euler-Jacobi pseudoprime F Factorial Factorial prime Faltings' theorem Farey sequence Fermat primality test Fermat's last theorem Fibonacci pseudoprime

F cont. Formula for primes Fundamental theorem of arithmetic G Gauss-Kuzmin-Wirsing operator Generalized continued fraction Generalized taxicab number Gilbreath's conjecture Goldbach's weak conjecture Golomb ruler Great Internet Mersenne Prime Search Greatest common divisor H Happy number Harmonic number Hasse's theorem on elliptic curves Hasse-Minkowski theorem Heegner number Highly abundant number Highly cototient number Highly totient number Hilbert's Theorem 90 Hyperperfect number I Ideal number Integer Integer factorization Integer partition Integer sequence Integer square root Integer-valued polynomial Interesting number paradox J Jacobi triple product K Khinchin's constant L Langlands program Legendre's constant Lenstra-Pomerance-Wagstaff conjecture Lindemann-Weierstrass theorem Liouville function List of mathematical functions List of number theory topics List of recreational number theory topics Local analysis Low-discrepancy sequence Lucas pseudoprime Lucas sequence Lucas-Carmichael number Lucky number Lucky prime Lévy's constant M Mahler's theorem Mersenne prime Mertens conjecture Mertens function Miller-Rabin primality test Multiplicative function Multiplicative group of integers modulo n Multiply perfect number Möbius function Möbius inversion formula N Natural number New Mersenne conjecture NewPGen Newman-Shanks-Williams prime Nontotient Normal number Number theory P P-adic number

P cont. Partition function (number theory) Pentagonal number theorem Perfect number Perrin pseudoprime Persistence of a number Practical number Primality test Prime desert Prime factor Prime factorization algorithm Prime number Prime pages Primeval number Probable prime Prouhet-Thue-Morse constant Pseudoprime Pythagorean triple Q Q-series Quadratic irrational Quadratic reciprocity Quasiperfect number Question mark function R Remainder S Schnorr group Self number Semiperfect number Semistable elliptic curve Sieve of Eratosthenes Skewes' number Smooth number Sociable number Solovay-Strassen primality test Somer-Lucas pseudoprime Special number field sieve Square-free Stirling's approximation Strong Lucas pseudoprime Strong pseudoprime Subfactorial Sumset Super-Poulet number Superabundant number Superior highly composite number Supersingular prime T Table of divisors Taxicab number Twin prime Twin prime conjecture U Ulam spiral V Viswanath's constant Von Staudt-Clausen theorem Vorlesungen über Zahlentheorie W Wagstaff prime Wall-Sun-Sun prime Waring's problem Weil conjectures Weird number Wieferich prime Wilson prime Wolstenholme prime Wolstenholme's theorem Z Znám's problem