Arithmetic theory of harmonic numbers

Author:
Zhi-Wei Sun

Journal:
Proc. Amer. Math. Soc. **140** (2012), 415-428

MSC (2010):
Primary 11B75; Secondary 05A19, 11A07, 11B68

Published electronically:
June 8, 2011

MathSciNet review:
2846311

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Abstract: Harmonic numbers play important roles in mathematics. In this paper we investigate their arithmetic properties and obtain various basic congruences. Let be a prime. We show that

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Additional Information

**Zhi-Wei Sun**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
zwsun@nju.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-2011-10925-0

Keywords:
Harmonic numbers,
congruences,
Bernoulli numbers

Received by editor(s):
July 22, 2010

Received by editor(s) in revised form:
November 23, 2010

Published electronically:
June 8, 2011

Additional Notes:
The author was supported by the National Natural Science Foundation (grant 10871087) of China

Communicated by:
Matthew A. Papanikolas

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.