Mao Hua LE
Let a be a positive integer. Let D = 3a2 + 1 and p = 4a2 + 1, where p is a prime. In this paper we prove that if a is not a multiple of 4, then the equation x2 + Dm = pn has exactly two solutions (x, m, n) = (a, 1,1) and (8a3 + 3a, 1,3), except for (D,p) = (4,5), in which case the equation has exactly three solutions (x,m, n) = (1,1,1), (3,2,2) and (11,1,3).