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

## Annual Meeting in Mathematics 2023

## 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

## How to Cite

*Thai Journal of Mathematics*,

*22*(1), 227–237. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1612