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In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by . used Kummer's congruences to define the p-adic zeta function. ==Statement== The simplest form of Kummer's congruence states that : where ''p'' is a prime, ''h'' and ''k'' are positive even integers not divisible by ''p''−1 and the numbers ''B''''h'' are Bernoulli numbers. More generally if ''h'' and ''k'' are positive even integers not divisible by ''p'' − 1, then : where φ(''p''''a''+1) is the Euler totient function, evaluated at ''p''''a''+1 and ''a'' is a non negative integer. At ''a'' = 0, the expression takes the simpler form, as seen above. The two sides of the Kummer congruence are essentially values of the p-adic zeta function, and the Kummer congruences imply that the ''p''-adic zeta function for negative integers is continuous, so can be extended by continuity to all ''p''-adic integers. 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「Kummer's congruence」の詳細全文を読む スポンサード リンク
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