Fermat's little theorem

English

Alternative forms

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Etymology

Template:Named-after, who stated a version of the theorem in a letter in 1640. Called little to distinguish it from Fermat's Last Theorem.

Proper noun

1. Template:Lb The theorem that, for any prime number $p$ and integer $a$, $a^p-a$ is an integer multiple of $p$.
   • 1999, John Stillwell, Translator's introduction, Template:W, Template:W (supplements), Lectures on Number Theory, [1863, P. G. Lejeune Dirichlet, R. Dedekind, Template:W], Template:W, 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, Template:W 1746, page 222,

     Most of the pseudoprimality tests originate in some sense on Fermat's Little Theorem aⁿ⁻¹ ≡ 1 mod n.

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Synonyms

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Translations

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See also

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Further reading

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