The Square Terms in Generalized Lucas Sequence with Parameters P And Q - Şi̇ar Zafer; Keski̇n Refi̇k (MATHEMATICA SCANDINAVICA, 2016)
Let P and Q be nonzero integers. Generalized Lucas sequence is defined as follows: V_0=2, V_1=P, and V_n+1=PV_n+QV_n-1 for n≥ 1. We assume that P and Q are odd relatively prime integers. Firstly, we determine all indices n such that V_n=kx^2 and V_n=2kx^2 when k|P. Then, as an application of our these results, we find all solutions of the equations V_n=3x^2 and V_n=6x^2. Moreover, we find integer solutions of some Diophantine equations.