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In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity. There is a rational reciprocity law for 8th powers, due to Williams. Define the symbol (''x''|''p'')''k'' to be +1 if ''x'' is a ''k''-th power modulo the prime ''p'' and -1 otherwise. Let ''p'' and ''q'' be distinct primes congruent to 1 modulo 8, such that (''p''|''q'') = (''q''|''p'') = +1. Let ''p'' = ''a''2 + ''b''2 = ''c''2 + 2''d''2 and ''q'' = ''A''2 + ''B''2 = ''C''2 + 2''D''2, with ''aA'' odd. Then : ==References== * * 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「Octic reciprocity」の詳細全文を読む スポンサード リンク
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