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arXiv · 1407.5789

A Curious Congruence Involving Alternating Harmonic Sums

Liuquan Wang
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Abstract

Let $p$ be a prime and ${\mathcal{P}_{p}}$ the set of positive integers which are prime to $p$. We establish the following interesting congruence \[\sum\limits_{\begin{smallmatrix} i+j+k={{p}^{r}} i,j,k\in {\mathcal{P}_{p}} \end{smallmatrix}}{\frac{{{(-1)}^{i}}}{ijk}}\equiv \frac{{{p}^{r-1}}}{2}{{B}_{p-3}}\, (\bmod \, {{p}^{r}}).\]

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Liuquan Wang. 2014-07-22. A Curious Congruence Involving Alternating Harmonic Sums. https://arxiv.org/abs/1407.5789

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