## Jiayuan Hu, Xiaoxue Li : On the generalized Ramanujan-Nagell equation with , 257-265

### Abstract:

Let be an odd prime, and let , be positive integers with . For any nonnegative integer , let and , where and . In this paper we prove the following results: (i) If , then and the equation has only the positive integer solution . (ii) If and with , then the equation has only the positive integer solution .

Key Words: exponential diophantine equation; generalized Ramanujan-Nagell equation; Pell number.

2010 Mathematics Subject Classification: 11D61.