On the Diophantine equation $c{x}^2+p^{2m}=4y^n$

Kalyan Chakraborty, Azizul Hoque, Kotyada Srinivas

Let $c$ be a square-free positive integer and $p$ a prime satisfying $p\nmid c$. Let $h(-c)$ denote the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-c})$. In th…