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A simple proof of a curious congruence by Zhao
Authors:Chun-Gang Ji
Institution:Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China
Abstract:The author gives a simple proof of the following curious congruence for odd prime $p>3$ which was established by Jianqiang Zhao:

\begin{displaymath}\sum _{\substack{{i+j+k=p} {i, j, k>0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{displaymath}

Keywords:Wolstenholme's theorem  Kummer congruence  prime number
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