More on the Quadratic Exponential Diophantine Equation $(p^k - 1)^x + (p^k)^y = z^2$: Annual Meeting in Mathematics 2024

Phornpassorn Boonchu; Janyarak Tongsomporn; Saeree Wananiyakul

More on the Quadratic Exponential Diophantine Equation $(p^k - 1)^x + (p^k)^y = z^2$

Annual Meeting in Mathematics 2024

Authors

Phornpassorn Boonchu
Janyarak Tongsomporn
Saeree Wananiyakul Chulalongkorn University

Keywords:

Catalan's conjecture (Milailescu's Theorem), exponential Diophantine equation, integer solutions

Abstract

We present completed proofs of determining the set of all solutions of the Diophantine equation in the title, which was first presented in 2015, for some fixed prime numbers p and unconditional for non-negative integers x, y.

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Published

2025-03-31

How to Cite

Boonchu, P., Tongsomporn, J., & Wananiyakul, S. (2025). More on the Quadratic Exponential Diophantine Equation $(p^k - 1)^x + (p^k)^y = z^2$: Annual Meeting in Mathematics 2024. Thai Journal of Mathematics, 23(1), 177–183. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1773