Factorials as repdigits in base b

Nurettin Irmak and Alain Togbé
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 21–25
DOI: 10.7546/nntdm.2022.28.1.21-25
Full paper (PDF, 178 Kb)

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Authors and affiliations

Nurettin Irmak
Department of Fundamental Science, Faculty of Engineering and Natural Science,
Konya Technical University, Konya, Turkey

Alain Togbé
Department of Mathematics, Purdue University Northwest
1401 S. U. S. 421., Westville, IN 46391, United States

Abstract

Let b\in \left\{ 2,3, \ldots,9\right\}. In this paper, we show that the solutions of the equation \left( x\right) _{b}=m! are \left( 11\right) _{5}=3!, \left( 33\right) _{7}=\left( 44\right)_{5}=4!, where \left( x\right) _{b} has at least two digits.

Keywords

  • Factorials
  • Repdigits
  • Diophantine equation

2020 Mathematics Subject Classification

  • 11D72
  • 11A07
  • 11B50

References

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Manuscript history

  • Received: 11 January 2021
  • Revised: 1 October 2022
  • Accepted: 17 January 2022
  • Online First: 6 February 2022

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Cite this paper

Irmak, N., & Togbé, A. (2022). Factorials as repdigits in base b. Notes on Number Theory and Discrete Mathematics, 28(1), 21-25, DOI: 10.7546/nntdm.2022.28.1.21-25.

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