Thai Journal of Mathematics, Volume 23, Issue 1, Pages 177-183 , 01/03/2025

More on the Quadratic Exponential Diophantine Equation (pk − 1)x + (pk)y = z2

Phornpassorn Boonchu, Janyarak Tongsomporn, Saeree Wananiyakul

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 nonnegative integers x, y.

Document Type

Article

Source Type

Journal

Keywords

Catalan’s conjecture (Milǎilescu’s Theorem)exponential Diophantine equationinteger solutions

ASJC Subject Area

Mathematics : Mathematics (all)

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Bibliography


Boonchu, P., Tongsomporn, J., & Wananiyakul, S. (2025). More on the Quadratic Exponential Diophantine Equation (pk − 1)x + (pk)y = z2. Thai Journal of Mathematics, 23(1) 177-183.

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