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In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers ''a'', ''b'', and ''c'' satisfy the equation ''a''''n'' + ''b''''n'' = ''c''''n'' for any integer value of ''n'' greater than two. The cases ''n'' = 1 and ''n'' = 2 were known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of ''Arithmetica'' where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the ''Guinness Book of World Records'' for "most difficult mathematical problems". ==Overview== Fermat's Last Theorem stood unsolved in mathematics for over three and a half centuries. Fermat wrote in the margin of a book that he had proved the deceptively simple theorem around 1637. His claim was discovered after his death some 30 years later, but with no proof provided. The claim eventually became one of the most notable unsolved problems of mathematics. Attempts to prove it prompted substantial development in number theory, and over time Fermat's Last Theorem gained prominence as an unsolved problem in mathematics. It is based on the Pythagorean theorem, which states that , where ''a'' and ''b'' are the lengths of the legs of a right triangle and ''c'' is the length of the hypotenuse. The Pythagorean equation has an infinite number of positive integer solutions for ''a'', ''b'', and ''c''; these solutions are known as Pythagorean triples. Fermat stated that the more general equation had no solutions in positive integers, if ''n'' is an integer greater than 2. Although he claimed to have a general proof of his conjecture, Fermat left no details of his proof apart from the special case ''n'' = 4. 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's Last Theorem」の詳細全文を読む スポンサード リンク
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