On the Ramanujan-Nagell type Diophantine equation x2+Akn=B

Let A, B be positive integers and q a prime. In this paper, we prove that the Ramanujan-Nagell type Diophantine equation x2+Aqn=B has at most four nonnegative integer solutions (x, n) for q2∤ B and B≥ C where C is some constant depending of A. We also prove that the equation x2+3×2n=B has at most four nonnegative integer solutions (x, n). Therefore, we partially confirm a conjecture of Ulas ([4])