“…In [1], the authors showed that when a ̸ = 0 and b ̸ = ∓2 are integers, the equation V n (P, ∓1) = ax 2 + b has only a finite number of solutions n. Moreover, the same authors showed that when a ̸ = 0 and b are integers, the equation U n (P, ±1) = ax 2 + b has only a finite number of solutions n. Keskin [14] solved the equation V n (P, −1) = wx 2 ∓ 1 for w = 1, 2, 3, 6 when P is odd. Keskin and Öğüt [15] solved the equations U n (P, −1) = wx 2 + 1 for w = 1, 2, 3, 5, 7, 10 when P is odd. Öğüt and Keskin [22] showed that only U 1 (P, −1) and U 2 (P, −1) may be of the form 11x 2 + 1 if P is odd.…”