Congruences involving alternating sums related to harmonic numbers and binomial coefficients

Laid Elkhiri, Miloud Mihoubi and Abdellah Derbal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 4, Pages 39–51
DOI: 10.7546/nntdm.2020.26.4.39-51
Full paper (PDF, 187 Kb)

Details

Authors and affiliations

Laid Elkhiri
Ibn Khaldoun University, EDPNLHM Laboratory of ENS
Old Kouba, Tiaret, Algeria

Miloud Mihoubi
USTHB, Faculty of Mathematics, RECITS Laboratory
PO Box 32 16111 El-Alia, Bab-Ezzouar, Algiers, Algeria

Abdellah Derbal
ENS, Department of Mathematics, EDPNLHM Laboratory
Old Kouba, Algiers, Algeria

Abstract

In 2017, Bing He investigated arithmetic properties to obtain various basic congruences modulo a prime for several alternating sums involving harmonic numbers and binomial coefficients. In this paper we study how we can obtain more congruences modulo a power of a prime number (super congruences) in the ring of -integer involving binomial coefficients and generalized harmonic numbers.

Keywords

• Binomial coefficients
• Harmonic numbers
• Generalized harmonic numbers
• Congruences

2010 Mathematics Subject Classification

• 11A07
• 11B65
• 11B99

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