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