Degenerate and n-adic versions of Kummer's congruences for values of Bernoulli polynomials

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• 作者：Young ; Paul Thomas
• 关键词：Bernoulli polynomials ; Degenerate Bernoulli polynomials ; Kummer congruences ; n-adic numbers
• 刊名：Discrete Mathematics
• 出版年：2004
• 出版时间：August 6, 2004
• 年：2004
• 卷：285
• 期：1-3
• 页码：289-296
• 全文大小：245 K

文摘

We first prove an analogue of Kummer's congruences for expressions involving the degenerate Bernoulli polynomials which were introduced by Carlitz, by relating them to the general theory of “degenerate number sequences” developed in a recent article. These congruences extend, for example, known congruences for the Genocchi numbers. We also give versions of Kummer's congruences modulo powers of a general positive integer n for Bernoulli polynomials with n-adic integer argument, and similar congruences for generalized Bernoulli polynomials, which extend recent results of Z.-W. Sun and of the author.