Note on some sequences having periods that divide (pp − 1) / (p − 1)

Abdelkader Benyattou and Miloud Mihoubi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 234—239
DOI: 10.7546/nntdm.2022.28.2.234-239
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Authors and affiliations

Abdelkader Benyattou
Department of Mathematics and Informatics, Zian Achour University of Djelfa, Algeria
RECITS Laboratory, P. O. 32 Box 32, El Alia 16111, Algiers, Algeria

Miloud Mihoubi
Faculty of Mathematics, USTHB
RECITS Laboratory, P. O. 32 Box 32, El Alia 16111, Algiers, Algeria

Abstract

In this paper, we use the properties of the classical umbral calculus to determine sequences related to the Bell numbers and having periods divide \left(p^{\,p}-1\right) / \left(p-1\right).

Keywords

  • Classical umbral calculus
  • Congruences
  • Bell numbers

2020 Mathematics Subject Classification

  • 05A40
  • 11A07
  • 11B73

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Manuscript history

  • Received: 7 June 2021
  • Revised: 9 March 2022
  • Accepted: 15 April 2022
  • Online First: 19 April 2022

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Cite this paper

Benyattou, A., & Mihoubi, M. (2022). Note on some sequences having periods that divide (pp − 1) / (p − 1). Notes on Number Theory and Discrete Mathematics, 28(2), 234-239, DOI: 10.7546/nntdm.2022.28.2.234-239.

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