On a kind of generilized multi-harmonic sum

Abstract

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

this is a wrong result and need to be corrected