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In number theory, Sophie Germain's theorem is a statement about the divisibility of solutions to the equation ''x''''p'' + ''y''''p'' = ''z''''p'' of Fermat's Last Theorem. ==Formal statement== Specifically, Sophie Germain proved that the product ''xyz'' must be divisible by ''p''2 if an auxiliary prime θ can be found such that two conditions are satisfied: # No two ''p''th powers differ by one modulo θ; and # ''p'' is itself not a ''p''th power modulo θ. Conversely, the first case of Fermat's Last Theorem (the case in which ''p'' does not divide ''xyz'') must hold for every prime ''p'' for which even one auxiliary prime can be found. 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「Sophie Germain's theorem」の詳細全文を読む スポンサード リンク
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