On special exponential Diophantine equations

Tomáš Riemel
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 598–602
DOI: 10.7546/nntdm.2023.29.3.598-602
Full paper (PDF, 165 Kb)

Details

Authors and affiliations

Tomáš Riemel
Department of Mathematics and Descriptive Geometry, Technical University of Ostrava
17. listopadu 2172/15, 708 00 Ostrava – Poruba, Czech Republic

Abstract

In this paper, we will focus on the study of a special type of exponential Diophantine equations, including a proof. The main contribution of this article is the mentioned type of equations, which can only be solved by the methods of elementary mathematics.

Keywords

  • Diophantine
  • Exponential
  • Equation
  • Elementary mathematics

2020 Mathematics Subject Classification

  • 11D61

References

  1. Cassels, J. W. S. (1953). On the equation a^x - b^y = 1. American Journal of Mathematics, 75(1), 159–162.
  2. Riemel, T. (2021). O exponenciálních diofantovských rovnicích. Matematika–Fyzika–Informatika, 30(2), 81–90.
  3. Riemel, T. (2022). Special exponential Diophantine equations. Proceedings of 15th annual International Conference of Education, Research and Innovation (ICERI2022), 7–11 November 2022, Seville, Spain, 15, 920–925.

Manuscript history

  • Received: 22 January 2023
  • Revised: 8 June 2023
  • Accepted: 17 August 2023
  • Online First: 25 August 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Related papers

Cite this paper

Riemel, T. (2023). On special exponential Diophantine equations. Notes on Number Theory and Discrete Mathematics, 29(3), 598-602, DOI: 10.7546/nntdm.2023.29.3.598-602.

Comments are closed.