Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

Abstract

It is well-known that for $p=1,2,3,7,11,19,43,67,163$, the class number of $\mathbb{Q}(\sqrt{-p})$ is one. We use this fact to determine all the solutions of $x^2+p^m=4y^n$ in non-negative integers $x,y,m$ and $n$.

12 pages. To appear in Publicationes Mathematicae Debrecen