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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simple proof of a curious congruence by Sun


Authors: Zun Shan and Edward T. H. Wang
Journal: Proc. Amer. Math. Soc. 127 (1999), 1289-1291
MSC (1991): Primary 11A07, 11A41
Published electronically: January 27, 1999
MathSciNet review: 1486751
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Abstract: In this note, we give a simple and elementary proof of the following curious congruence which was established by Zhi-Wei Sun:

\begin{displaymath}\sum^{(p-1)/2}_{k=1}\frac{1}{k\cdot 2^k}\equiv\sum^{[3p/4]}_{k=1} \frac{(-1)^{k-1}}{k}\quad(\mathrm{mod}\,p).\end{displaymath}


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Additional Information

Zun Shan
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210097, People’s Republic of China

Edward T. H. Wang
Affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5
Email: ewang@machl.wlu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04816-9
PII: S 0002-9939(99)04816-9
Received by editor(s): August 13, 1997
Published electronically: January 27, 1999
Communicated by: David Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society