Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11A07, 11A41

Retrieve articles in all journals with MSC (1991): 11A07, 11A41

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

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia