On Cubic Exponential Diophantine Equations $\pm 3^x \pm a^y = z^3$

Annual Meeting in Mathematics 2023

Authors

  • Poonyanoot Khanom
  • Saeree Wananiyakul
  • Janyarak Tongsomporn Walailak University

Keywords:

Catalan's conjecture, cubic diophantine equations, exponential diophantine equations

Abstract

We investigate the integer solutions of the cubic exponential Diophantine equations in the form $\pm 3^x \pm a^y = z^3$ using elementary techniques. In particular, we also prove that there are infinitely many cubic exponential Diophantine equations in that form that have no integer solutions.

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Published

2024-03-31 — Updated on 2024-03-31

How to Cite

Khanom, P., Wananiyakul, S., & Tongsomporn, J. (2024). On Cubic Exponential Diophantine Equations $\pm 3^x \pm a^y = z^3$: Annual Meeting in Mathematics 2023. Thai Journal of Mathematics, 22(1), 227–237. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1612

Issue

Vol. 22 No. 1 (2024): March

Section

Articles