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Somnuk Srisawat, Wanna Sriprad,
On the Diophantine equation a^x+b^y=z^2 where a\equiv 1 (mod 3) and b\equiv 1 (mod 3).
Int. J. Math. Comput. Sci., 20, no. 2, (2025), 637-639

DOI:

https://doi.org/10.69793/ijmcs/02.2025/wanna

Keywords and phrases:

Diophantine equation, congruence.

Abstract:

In this article, we show that the Diophantine equation a^x+b^y=z^2 has no non-negative integer solution, where a,b are positive odd integers with a\equiv 1 (mod 3), b\equiv 1 (mod 3), and x, y, z are non-negative integers.