On the Diophantine equation 3^x-2.5^y=z^2
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Abstract
In 2022, Gope and Masud proved that the Diophantine equation has no non-negative integer solution. After studying, we found that the Diophantine equation
has a non-negative integer solution. Thus, in this article, we show that the Diophantine equation
has exactly two non-negative integer solutions
, which are
and
, by using basic knowledge of number theory. Moreover, the results can also be extended to other related forms of Diophantine equations, such as multiples of X, Y+1, multiples of Z2n and .
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References
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