On the Lucas sequence equations V-n(P, 1) = wkx(2), w epsilon {5,7}

Abstract

Let P be an odd integer and (V-n) denote the generalized Lucas sequence defined by V-0 = 2, V-1 = P, and Vn+1 = PVn + Vn-1 for n >= 1. In this study, we solve the equations V-n = 5kx(2), V-n = 7kx(2), V-n = 5kx(2) +/- 1, and V-n = 7kx2 +/- 1 when k|P with k > 1. Moreover, applying some of the results, we obtain complete solutions to the equations Vn = sigma x(2), sigma epsilon {15, 21, 35}.