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arXiv · 2511.23308

On a kind of generalized multi-harmonic sums

Jiaqi Wang·Rong Ma
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Abstract

Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence, which is $$ \sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n$-th Bernoulli number. In this paper, we will generalize this kind of sums and prove a family of similar congruences modulo prime powers $p^r$.

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Jiaqi Wang, Rong Ma. 2025-12-02. On a kind of generalized multi-harmonic sums. https://arxiv.org/abs/2511.23308

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