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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

Online
ISSN
1337-2211
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Volume 68, Issue 5

Issues

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

Abstract

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

i+j+k=pri,j,kPp1ijk-2pr-1Bp-3(modpr),

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,

i+j+k=pαqβi,j,kP2pq1ijk78(2-q)(1-1q3)pα-1qβ-1Bp-3(modpα)

and

i+j+k=pαqβi,j,kPpq(-1)iijk12(q-2)(1-1q3)pα-1qβ-1Bp-3(modpα).

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)

References

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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