Some families of supercongruences involving alternating multiple harmonic sums
Volume 185 / 2018
Acta Arithmetica 185 (2018), 201-210
MSC: 11A07, 11B68.
DOI: 10.4064/aa170306-13-5
Published online: 6 July 2018
Abstract
Let $p$ be a prime. We study some families of supercongruences involving the alternating sums \begin{equation*} \sum_{\substack{j_1+\cdots+j_n=2 p^r \\ p\nmid j_1 \ldots j_n }} \frac{(-1)^{j_1+\cdots+j_b}}{j_1\ldots j_n} {\rm mod}\ {p^r}, \end{equation*} and extend similar statements proved by Shen and Cai who treated the cases when $n=4,5$. Our method works for arbitrary $n$.
