Fermat's little theorem

== English == === Alternative forms === Fermat's Little Theorem === Etymology === Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665), who stated a version of the theorem in a letter in 1640. Called little to distinguish it from Fermat's Last Theorem. === Proper noun === Fermat's little theorem (number theory) The theorem that, for any prime number p {\displaystyle p} and integer a {\displaystyle a} , a p − a {\displaystyle a^{p}-a} is an integer multiple of p {\displaystyle p} . 1999, John Stillwell, Translator's introduction, Peter Gustav Lejeune Dirichlet, Richard Dedekind (supplements), Lectures on Number Theory, [1863, P. G. Lejeune Dirichlet, R. Dedekind, Vorlesungen über Zahlentheorie], American Mathematical Society, page xi, When combined with the historical remarks made by Gauss himself, they give a bird's eye view of number theory from approximately 1640 to 1840 - from Fermat's little theorem to L-functions - the period which produced the problems and ideas which are still at the center of the subject. 1999, Siguna Müller, On the Combined Fermat/Lucas Probable Prime Test, Michael Walker (editor), Cryptography and Coding: 7th IMA International Conference, Springer, LNCS 1746, page 222, Most of the pseudoprimality tests originate in some sense on Fermat's Little Theorem an−1 ≡ 1 mod n. ==== Synonyms ==== (theorem that a p − a is divisible by p): Fermat's theorem ==== Translations ==== === See also === Euler's totient function === Further reading === Euler's theorem on Wikipedia.Wikipedia Fermat pseudoprime on Wikipedia.Wikipedia