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Mathematica Slovaca

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Volume 68, Issue 5


Congruences involving alternating harmonic sums modulo pα qβ

Zhongyan Shen / Tianxin Cai
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0159


In 2014, Wang and Cai established the following harmonic congruence for any odd prime p and positive integer r,


where Pn denote the set of positive integers which are prime to n.

In this note, we obtain the congruences for distinct odd primes p, q and positive integers α, β,




MSC 2010: Primary 11A07, 11A41

Keywords: Bernoulli numbers; harmonic sums; congruences

This work is supported by the Natural Science Foundation of Zhejiang Province, Project (No. LY18A010016) and the National Natural Science Foundation of China, Project (No. 11571303)


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About the article

Received: 2017-01-02

Accepted: 2017-05-30

Published Online: 2018-10-20

Published in Print: 2018-10-25

Communicated by Federico Pellarin

Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 975–980, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0159.

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