Word.ws English Dictionary

Fermat's little theorem

Fermat's little theorem proper noun: the theorem that, for any prime number p and integer a, aᵖ-a is an integer multiple of p.

Proper noun

Fermat's little theorem

  1. The theorem that, for any prime number p and integer a, aᵖ-a is an integer multiple of p.
    • 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, John Stillwell, Translator's introduction, Peter Gustav Lejeune Dirichlet, Richard Dedekind (supplements), Lectures on Number Theory, [1863, P. G. Lejeune Dirichlet, R. Dedekind, Vorlesungen...
    • Most of the pseudoprimality tests originate in some sense on Fermat's Little Theorem aⁿ⁻¹ ≡ 1 mod n.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
    Synonyms:
    theorem that a p − a is divisible by p

Synonyms of Fermat's little theorem

  • theorem that a p − a is divisible by p

Forms of Fermat's little theorem

alternative formFermat's Little Theorem

Origin of Fermat's little theorem

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.

Questions about Fermat's little theorem

What does Fermat's little theorem mean?
Fermat's little theorem means the theorem that, for any prime number p and integer a, aᵖ-a is an integer multiple of p.
What part of speech is Fermat's little theorem?
Fermat's little theorem is a proper noun.

Words near Fermat's little theorem in the dictionary

  1. Fermat prime
  2. Fermat primes
  3. Fermat pseudoprime
  4. Fermat pseudoprimes
  5. Fermat's Last Theorem
  6. Fermat's little theorem
  7. Fermat's principle
  8. Fermat's principle of least time
  9. Fermat-Apollonius circle
  10. Fermat-Apollonius circles
  11. Fermat-Torricelli point

Source and license

Adapted from Wiktionary: Fermat's little theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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