The solutions of the Diophantine equations 〖11〗^x-3^y=z^2 and 〖14〗^x-3^y=z^2
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Abstract
In this paper, we study all solutions of the Diophantine equations and
, where
and
are non-negative integers. By using the elementary concepts of congruence and Mihăilescu’s Theorem, we show that the Diophantine equation
has the unique non-negative integer solution
, which is
. The Diophantine equation
has exactly two non-negative integer solutions
, which are
and
.
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References
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