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All Number Theory

Proved results about the integers and their properties. Belongs here: theorems in elementary or analytic number theory. Does not belong here: unproved number-theoretic claims, filed under the Conjectures category instead.

15 and 290 Theorems

Albert-Brauer-Hasse-Noether Theorem

Ankeny-Artin-Chowla Congruence

Apery's Theorem

Artin Reciprocity Law

Artin-Verdier Duality

Baker's Theorem

Barban-Davenport-Halberstam Theorem

Behrend's Theorem

Bertrand's Postulate

Bezout's Identity

Bhaskara's Lemma

Birch's Theorem

Bombieri-Vinogradov Theorem

Brauer-Siegel Theorem

Brun's Theorem

Brun-Titchmarsh Theorem

Carmichael's Theorem

Cassini and Catalan Identities

Chebotarev Density Theorem

Chen's Theorem

Chevalley-Warning Theorem

Chinese Remainder Theorem

Chowla-Mordell Theorem

Class Number Formula

Cohn's Irreducibility Criterion

Davenport-Schmidt Theorem

Decimal Representation

Dirichlet's Approximation Theorem

Dirichlet's Theorem on Arithmetic Progressions

Dirichlet's Unit Theorem

Equidistribution Theorem

Erdos-Ginzburg-Ziv Theorem

Erdos-Kac Theorem

Euclidean Division

Euclid-Euler Theorem

Euclid's Lemma

Euclid's Theorem

Euler Brick

Euler's Criterion

Euler's Theorem (Totient)

Faltings's Theorem

Fermat's Last Theorem

Fermat's Little Theorem

Fermat's Polygonal Number Theorem

Fermat's Theorem on Sums of Two Squares

Ferrero-Washington Theorem

Friedlander-Iwaniec Theorem

Fueter-Polya Theorem

Fundamental Theorem of Arithmetic

Furstenberg's Proof of the Infinitude of Primes

Gauss Congruence

Gelfond-Schneider Theorem

Glaisher's Theorem

Green-Tao Theorem

Grunwald-Wang Theorem

Hardy-Ramanujan Theorem

Hasse Norm Theorem

Hasse-Minkowski Theorem

Hasse's Theorem on Elliptic Curves

Herbrand-Ribet Theorem

Hilbert's Irreducibility Theorem

Hilbert-Speiser Theorem

Hilbert-Waring Theorem

Hurwitz's Theorem (Number Theory)

Infinitude of Primes

Jacobi's Four-Square Theorem

Jurkat-Richert Theorem

Kaplansky's Theorem on Quadratic Forms

Kronecker's Approximation Theorem

Kronecker-Weber Theorem

Kummer's Theorem

Lafforgue's Theorem

Lagrange's Four-Square Theorem

Landau Prime Ideal Theorem

Law of Quadratic Reciprocity

Legendre's Three-Square Theorem

Lindemann-Weierstrass Theorem

Linnik's Theorem

Liouville's Approximation Theorem