A generalization of a curious congruence on harmonic sums

Authors:
Xia Zhou and Tianxin Cai

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1329-1333

MSC (2000):
Primary 11A07, 11A41

DOI:
https://doi.org/10.1090/S0002-9939-06-08777-6

Published electronically:
December 28, 2006

MathSciNet review:
2276641

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Zhao established a curious harmonic congruence for prime :

**1.**Chun-Gang Ji,*A Simple Proof of A Curious Congruence By Zhao.**Proceedings of The American Mathematical Society*,**133**(2005):3469-3472. MR**2163581 (2006d:11005)****2.**J.W.L. Glaisher,*On the residues of the sums of products of the first p-1 numbers, and their powers, to modulus or .**Quart. J. Pure Appl. Math.,***31**(1900): 321-353.**3.**J.W.L. Glaisher,*On the residues of the inverse powers of numbers in arithmetic progression.**Quart. J. Pure Appl. Math.,***32**(1901):271-305.**4.**E. Lehmer,*On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson.**Ann. Math.,***39**(1938):350-360. MR**1503412****5.**Zhihong Sun,*Congruence concerning Bernoulli numbers and Bernoulli polynomials,**Discrete Applied Mathematics,***105**(2000):193-223. MR**1780472 (2001m:11022)****6.**L.C. Washington,*Introduction to Cyclotomic Fields, 2nd ed.,*Springer-Verlag, New York, 1997. MR**1421575 (97h:11130)****7.**Jiangqiang Zhao,*Bernoulli numbers, Wolstenholme's Theorem, and variations of Lucas' Theorem,*arxiv.org/abs/math.NT/0303332**8.**Jiangqiang Zhao,*Multiple Harmonic Sums I: Generalizations of Wolstenholme's Theorem,*xxx.lanl.gcv/abs/math.NT/0301252

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Additional Information

**Xia Zhou**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Email:
unitqq@zju.edu.cn

**Tianxin Cai**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Email:
txcai@mail.hz.zj.cn

DOI:
https://doi.org/10.1090/S0002-9939-06-08777-6

Keywords:
Bernoulli numbers,
congruences of harmonic sums,
partitions

Received by editor(s):
December 14, 2005

Received by editor(s) in revised form:
February 6, 2006

Published electronically:
December 28, 2006

Additional Notes:
This work was supported by the National Natural Science Foundation of China, Project 10371107

Communicated by:
Wen-Ching Winnie Li

Article copyright:
© Copyright 2006
American Mathematical Society