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THE UNIVERSAL KUMMER CONGRUENCES
Published online by Cambridge University Press: 22 March 2013
Abstract
Let $p$ be a prime. In this paper, we present a detailed $p$-adic analysis on 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 ${B}_{n} / n$ 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 ${B}_{n} / n$ when $n$ is divisible by $p- 1$.
Keywords
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 94 , Issue 1 , February 2013 , pp. 106 - 132
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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