On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\)

Abstract

In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\) has at most three nonnegative integer solutions \((x, n)\) for \(k\) a prime and \(B, D\) positive integers.