Fermat's little theorem

English Alternative forms en Fermat's Little Theorem Etymology en Pierre de Fermat 1601 1665 French lawyer and amateur mathematician =, who stated a version of the theorem in a letter in 1640. Called little to distinguish it from Fermat's Last Theorem. Proper noun en number theory The theorem that, for any prime number and integer , is an integer multiple of . 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, Lecture Notes in Computer Science LNCS 1746, page 222, Most of the pseudoprimality tests originate in some sense on Fermat's Little Theorem an−1 ≡ 1 mod n. en 2007 Thomas Koshy Elementary Number Theory with Applications Elsevier (Academic Press) 2nd https://books.google.com.au/books?id=d5Z5I3gnFh0C&pg=PA327&dq=%22Fermat%27s+little+theorem%22&hl=en&sa=X&ved=0ahUKEwiI0cbI48nWAhWDwrwKHTALDeYQ6AEISjAH#v=onepage&q=%22Fermat's%20little%20theorem%22&f=false 327 Incidentally, the special case of Fermat's little theorem for a = 2 was known to the Chinese as early as 500 B.C.The first proof of Fermat's little theorem was given by Euler in 1736, almost a century after Fermat's announcement. en 2008 Lawrence C. Washington Elliptic Curves: Number Theory and Cryptography Taylor & Francis (Chapman & Hall/CRC) 2nd https://books.google.com.au/books?id=nBfCEqpYKW0C&pg=PA189&dq=%22Fermat%27s+little+theorem%22&hl=en&sa=X&ved=0ahUKEwiI0cbI48nWAhWDwrwKHTALDeYQ6AEIggQwUA#v=onepage&q=%22Fermat's%20little%20theorem%22&f=false 189 Fermat's little theorem says that if n is prime and gcd(a,n) = 1, then an−1 ≡ 1 (mod n), so it follows that n must be composite, even though we have not produced a factor. Synonyms theorem that a p − a is divisible by p en Fermat's theorem Translations theorem that ap − a is divisible by p French: fr petit théorème de Fermat Hungarian: hu kis Fermat-tétel Italian: it piccolo teorema di Fermat m Russian: ru малая теорема Ферма See also en Euler's totient function Further reading Euler's theorem Fermat pseudoprime en eponyms