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William S. Gayo, Jr., Ronica M. de Leon, Regan R. Rola,
Non-existence of Solution of the Diophantine Equation 19^x+18^y=z^2.
Int. J. Math. Comput. Sci., 20, no. 4, (2025), 1029-1031.

DOI:

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

Keywords and phrases:

Diophantine equation, integer solutions, Mihailescu's Theorem, primes, Pythagorean triples, unsolvable.

Abstract:

In this paper, we show the non-existence of non-negative integer solution of the Diophantine equation 19^x+18^y=z^2.