M. Alan

A Note on a Lebesgue-Ramanujan-Nagell Type Diophantine Equation

We determine all solutions of \[ x^2+3^a7^b37^c=\lambda y^n, \] where $\lambda\in\{1,2,4\}$, $x,y\geq1$, $a,b,c\geq0$, $n\geq3$, and $\gcd(x,y)=1$, subject to the following parity condition: when $\lambda\in\{1,2\}$ and neither $3$ nor $4$ divides $n$, the integer $y$ is assumed to be odd. The cases divisible by $3$ or...