A simple proof of a curious congruence by Zhao

The author gives a simple proof of the following curious congruence for odd prime p>3 which was established by Jianqiang Zhao: \begin{equation*}\sum _{\substack{{i+j+k=p} {i, j, k>0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{equation*}

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-12, Vol.133 (12), p.3469-3472
Main Author: JI, Chun-Gang
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Exact sciences and technology
Integers
Mathematical congruence
Mathematical theorems
Mathematics
Number theory
Sciences and techniques of general use
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Summary:The author gives a simple proof of the following curious congruence for odd prime p>3 which was established by Jianqiang Zhao: \begin{equation*}\sum _{\substack{{i+j+k=p} {i, j, k>0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{equation*}
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07939-6