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- Title
THE UNIVERSAL KUMMER CONGRUENCES.
- Authors
HONG, SHAOFANG; ZHAO, JIANRONG; ZHAO, WEI
- 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 $p- 1$.
- Subjects
CONGRUENCES &; residues; GEOMETRIC congruences; DIFFERENTIAL geometry; BERNOULLI numbers; KUMMER surfaces
- Publication
Journal of the Australian Mathematical Society, 2013, Vol 94, Issue 1, p106
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788712000493