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arXiv · 1702.08599

Some Families of Super Congruences Involving Alternating Multiple Harmonic Sums

Kevin Chen·Rachael Hong·Jerry Qu·David Wang·Jianqiang Zhao
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Abstract

Let $p$ be a prime. In this short note we study some families of super congruences involving the following alternating sums \begin{equation*} \sum_{\substack{j_1+j_2+\cdots+j_n=2 p^r p\nmid j_1 j_2 \cdots j_n}} \frac{(-1)^{j_1+\cdots+j_b}}{j_1\cdots j_n} \pmod{p^r}, \end{equation*} which extend similar statements proved by Shen and Cai who treated the cases when $n=4,5$.

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Kevin Chen, Rachael Hong, Jerry Qu, David Wang, Jianqiang Zhao. 2018-05-13. Some Families of Super Congruences Involving Alternating Multiple Harmonic Sums. https://doi.org/10.4064/aa170306-13-5

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