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In number theory, Wilson's theorem states that a natural number ''n'' > 1 is a prime number if and only if :. That is, it asserts that the factorial is one less than a multiple of ''n'' exactly when ''n'' is a prime number. ==History== This theorem was stated by Ibn al-Haytham (c. 1000 AD), and John Wilson.〔Edward Waring, ''Mediationes Algebraicae'' (Cambridge, England: 1770), page 218 (in Latin). In the third (1782) edition of Waring's ''Mediationes Algebraicae'', Wilson's theorem appears as problem 5 on (page 380 ). On that page, Waring states: "Hanc maxime elegantem primorum numerorum proprietatem invenit vir clarissimus, rerumque mathematicarum peritissimus Joannes Wilson Armiger." (A man most illustrious and most skilled in mathematics, Squire John Wilson, found this most elegant property of prime numbers.)〕 Edward Waring announced the theorem in 1770, although neither he nor his student Wilson could prove it. Lagrange gave the first proof in 1771.〔Joseph Louis Lagrange, ("Demonstration d'un théorème nouveau concernant les nombres premiers" ) (Proof of a new theorem concerning prime numbers), ''Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres'' (Berlin), vol. 2, pages 125–137 (1771).〕 There is evidence that Leibniz was also aware of the result a century earlier, but he never published it.〔Giovanni Vacca (1899) "Sui manoscritti inediti di Leibniz" (On unpublished manuscripts of Leibniz), ''Bollettino di bibliografia e storia delle scienze matematiche'' ... (Bulletin of the bibliography and history of mathematics), vol. 2, pages 113–116; see (page 114 ) (in Italian). Vacca quotes from Leibniz's mathematical manuscripts kept at the Royal Public Library in Hanover (Germany), vol. 3 B, bundle 11, page 10: ''Original'' : Inoltre egli intravide anche il teorema di Wilson, come risulta dall'enunciato seguente: ''Translation'' : In addition, he () also glimpsed Wilson's theorem, as shown in the following statement:See also: Giuseppe Peano, ed., ''Formulaire de mathématiques'', vol. 2, no. 3, (page 85 ) (1897).〕 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「Wilson's theorem」の詳細全文を読む スポンサード リンク
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