A simple proof of a curious congruence by Zhao
Chun-Gang Ji · Proceedings of the American Mathematical Society · 2005
The author gives a simple proof of the following curious congruence for odd prime p > 3 p>3 which was established by Jianqiang Zhao: ∑ i + j + k = p i , j , k > 0 1 i j k ≡ − 2 B p − 3 ( mod p ) . \begin{equation*}\sum _{\substack {{i+j+k=p} {i,\ j,\ k>0}}}\frac {1}{ijk}\equiv -2B_{p-3}(\text {mod}\ p).\end{equation*}