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arXiv · 2411.03148

On a kind of generilized multi-harmonic sum

Jiaqi Wang·Rong Ma
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Abstract

Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence $$ \sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , $$ where $B_{n}$ denotes the $n-$th Bernoulli numbers. In this paper, we will generalize this problem by using congruent theory and combinatorial methods, and we get some curious congruences.

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Jiaqi Wang, Rong Ma. 2024-11-05. On a kind of generilized multi-harmonic sum. https://arxiv.org/abs/2411.03148

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