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A simple proof of a curious congruence by Zhao

Author: Chun-Gang Ji
Journal: Proc. Amer. Math. Soc. 133 (2005), 3469-3472
MSC (2000): Primary 11A07, 11A41
Published electronically: June 8, 2005
MathSciNet review: 2163581
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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}

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Additional Information

Chun-Gang Ji
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing 210097, People’s Republic of China
Address at time of publication: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Keywords: Wolstenholme's theorem, Kummer congruence, prime number
Received by editor(s): December 1, 2003
Received by editor(s) in revised form: August 13, 2004
Published electronically: June 8, 2005
Additional Notes: This work was supported by the National Natural Science Foundation of China, Grant Nos. 10171046 and 10201013
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.