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

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## 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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## Cite this paper

Elkhiri, L., Mihoubi, M., & Derbal, A. (2020). Congruences involving alternating sums related to harmonic numbers and binomial coefficients, 26(4), 39-51, doi: 10.7546/nntdm.2020.26.4.39-51.