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In mathematics, a Wieferich pair is a pair of prime numbers ''p'' and ''q'' that satisfy :''p''''q'' − 1 ≡ 1 (mod ''q''2) and ''q''''p'' − 1 ≡ 1 (mod ''p''2) Wieferich pairs are named after German mathematician Arthur Wieferich. Wieferich pairs play an important role in Preda Mihăilescu's 2002 proof of Mihăilescu's theorem (formerly known as Catalan's conjecture).〔Jeanine Daems (A Cyclotomic Proof of Catalan's Conjecture ).〕 == Known Wieferich pairs == There are only 7 Wieferich pairs known:〔, For example, currently there are two known double Wieferich prime pairs (p, q) with q = 5: (1645333507, 5) and (188748146801, 5).〕 :(2, 1093), (3, 1006003), (5, 1645333507), (5, 188748146801), (83, 4871), (911, 318917), and (2903, 18787). (sequences , and in OEIS) 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「Wieferich pair」の詳細全文を読む スポンサード リンク
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