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ON TWO DIOPHANTINE EQUATIONS $7^x + 19^y = z^2$ and $7^x + 91^y = z^2$
In this paper, we prove that both two Diophantine equations 7 x + 19 y = z 2 and 7 x + 91 y = z 2 have no non-negative integer solution where x, y and z are non-negative integers.