On the Diophantine equation $2+(m^2-2)^x=y^2$
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7268Keywords:
Diophantine Equations, Exponential Diophantine Equations, Quadratic Diophantine Equation.Abstract
This paper establishes conditions under which the Diophantine equation $2+(m^2-2)^x=y^2$ has exactly one solution in non-negative integers. As applications, we show that $2+7^x=y^2$ and $2+23^x=y^2$ have exactly one solution, namely $(x,y)=(1,3)$ and $(1,5)$, respectively.
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Copyright (c) 2026 Supawadee Prugsapitak, Phitchayawee Sangjan
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