A simple proof of a curious congruence by Sun
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- by Zun Shan and Edward T. H. Wang PDF
- Proc. Amer. Math. Soc. 127 (1999), 1289-1291 Request permission
Abstract:
In this note, we give a simple and elementary proof of the following curious congruence which was established by Zhi-Wei Sun: \[ \sum ^{(p-1)/2}_{k=1}\frac {1}{k\cdot 2^k}\equiv \sum ^{[3p/4]}_{k=1} \frac {(-1)^{k-1}}{k}\quad (\mathrm {mod} p).\]References
- Louis Comet, Advanced Combinatorics, D. Reidel Publishing Company, 1974.
- G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960.
- Winfried Kohnen, A simple congruence modulo $p$, Amer. Math. Monthly 104 (1997), no. 5, 444–445. MR 1447978, DOI 10.2307/2974738
- Zhi Wei Sun, A congruence for primes, Proc. Amer. Math. Soc. 123 (1995), no. 5, 1341–1346. MR 1242105, DOI 10.1090/S0002-9939-1995-1242105-X
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
- Received by editor(s): August 13, 1997
- Published electronically: January 27, 1999
- Communicated by: David Rohrlich
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1289-1291
- MSC (1991): Primary 11A07, 11A41
- DOI: https://doi.org/10.1090/S0002-9939-99-04816-9
- MathSciNet review: 1486751