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arXiv · 0808.3544

The universal Kummer congruences

Shaofang Hong·Jianrong Zhao·Wei Zhao
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Abstract

Let $p$ be a prime. In this paper, we present a detailed $p$-adic analysis to factorials and double factorials and their congruences. We give good bounds for the $p$-adic sizes of the coefficients of the divided universal Bernoulli number ${{\hat B_n}\over n}$ when $n$ is divisible by $p-1$. Using these we then establish the universal Kummer congruences modulo powers of a prime $p$ for the divided universal Bernoulli numbers ${{\hat B_n}\over n}$ when $n$ is divisible by $p-1$.

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Shaofang Hong, Jianrong Zhao, Wei Zhao. 2012-07-03. The universal Kummer congruences. https://arxiv.org/abs/0808.3544

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