The Solution of The Exponential Diophantine Equation 7^x - 5^y = z^2
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Abstract
In this paper, we prove that the exponential Diophantine equation has one solution where
and
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
.
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References
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