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In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. == Definition == Fermat's little theorem states that if ''p'' is prime and ''a'' is coprime to ''p'', then ''a''''p''−1 − 1 is divisible by ''p''. For an integer ''a'' > 1, if a composite integer ''x'' divides ''a''''x''−1 − 1, then ''x'' is called a Fermat pseudoprime to base ''a''. In other words, a composite integer is a Fermat pseudoprime to base ''a'' if it successfully passes the Fermat primality test for the base ''a''. It follows that if ''x'' is a Fermat pseudoprime to base ''a'', then ''x'' is coprime to ''a''. The smallest base-2 Fermat pseudoprime is 341. It is not a prime, since it equals 11·31, but it satisfies Fermat's little theorem: 2340 ≡ 1 (mod 341) and thus passes the Fermat primality test for the base 2. Pseudoprimes to base 2 are sometimes called Poulet numbers, after the Belgian mathematician Paul Poulet, Sarrus numbers, or Fermatians . A Fermat pseudoprime is often called a pseudoprime, with the modifier Fermat being understood. An integer ''x'' that is a Fermat pseudoprime for all values of ''a'' that are coprime to ''x'' is called a Carmichael number.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fermat pseudoprime」の詳細全文を読む スポンサード リンク
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