# The Solution of The Exponential Diophantine Equation 7^x - 5^y = z^2

## Abstract

In this paper, we prove that the exponential Diophantine equation  $7^x&space;-&space;5^y&space;=z^2$  has one solution where $x,&space;y$  and $z$ are non-negative integers. In the proof, we apply reasonably Catalan’s conjecture and various theories concerning the congruence to obtain the solution. The result reveals that the unique solution is $(x,y,z)=(0,0,0)$.

## Article Details

How to Cite
Thongnak, S., Chuayjan, W., & Kaewong, T. (2021). The Solution of The Exponential Diophantine Equation 7^x - 5^y = z^2. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 66(703), 62–67. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/240207
Section
Research Article

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