Some Families of Super Congruences Involving Alternating Multiple Harmonic Sums

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 $n=4,5$.

10 pages, Acta Arithmetica, 2018

References in corpus (5)

• A congruence involving harmonic sums modulo $p^{\alpha }{q}^{\beta }$
• Congruences Involving Multiple Harmonic Sums and Finite Multiple Zeta Values
• New Congruences on Multiple Harmonic Sums and Bernoulli Numbers
• Super congruences involving alternating harmonic sums modulo prime powers
• Super Congruences Involving Multiple Harmonic Sums and Bernoulli Numbers