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Nongnuch Saengsura, Rujisaya Yompadcha, Krittika Linesawat,

Solutions of the Diophantine Equation 2^x+63^y=z^2.

Int. J. Math. Comput. Sci., Volume 20, no. 4, (2025), 987-990.

DOI:

https://doi.org/10.69793/ijmcs/04.2025/saengsura

Keywords and phrases:

Diophantine equation, Catalan's Conjecture.

Abstract:

In this article, we show that the Diophantine equation 2^x+63^y=z^2 has exactly three solutions (x, y, z)=(0, 1, 8), (3, 0, 3), and (8, 2, 65) when x, y, and z are non-negative integers.