On a kind of generalized multi-harmonic sums

Jiaqi Wang, Rong Ma

Let $p$ be an odd prime, Jianqiang Zhao has established a curious congruence, which is $$\sum _{\genfrac{}{}{0ex}{}{i+j+k=p}{i,j,k>0}}\frac{1}{ijk}\equiv -2B_{p-3}(\mathrm{mod}p),$$ where $B_n$ de…