On a class of Lebesgue-Ljunggren-Nagell type equations

Andrzej Dąbrowski, Nursena Günhan, Gökhan Soydan

Given odd, coprime integers $a$, $b$ ($a>0$), we consider the Diophantine equation $a{x}^2+b^{2l}=4y^n$, $x,y\in \mathbb{Z}$, $l\in \mathbb{N}$, $n$ odd prime, $\gcd (x,y)=1$. We completely…