English

On a kind of generilized multi-harmonic sum

Number Theory 2025-12-03 v2 Combinatorics

Abstract

Let pp be an odd prime, Jianqiang Zhao has established a curious congruence i+j+k=pi,j,k>01ijk2Bp3(modp), \sum_{i+j+k=p \atop i,j,k > 0} \frac{1}{ijk} \equiv -2B_{p-3}\pmod p , where BnB_{n} denotes the nn-th Bernoulli numbers. In this paper, we will generalize this problem by using congruent theory and combinatorial methods, and we get some curious congruences.

Keywords

Cite

@article{arxiv.2411.03148,
  title  = {On a kind of generilized multi-harmonic sum},
  author = {Jiaqi Wang and Rong Ma},
  journal= {arXiv preprint arXiv:2411.03148},
  year   = {2025}
}

Comments

this is a wrong result and need to be corrected

R2 v1 2026-06-28T19:48:59.769Z