ON GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wkx2 ± 1

摘要

Let P be an odd integer, (Un) and (Vn) denote generalized Fibonacci and Lucas sequences defined by U0 = 0, U1 = 1, and Un+1 = PUn +Un1, V0 = 2, V1 = P, and Vn+1 = PVn + Vn1 for n 1. In this paper, we solve the equations Un = kx2 ± 1 under some conditions on n. Moreover, we determine all indices n such that the equations Vn = wkx2 ± 1, where w 2 {1, 2, 3, 6} , k|P with k > 1, have solutions.