MMN-1328
On the Equations $U_{n}=5$ and $V_{n}=5$
Abstract
Let P≥3 be an integer and let (U_{n}) and (V_{n}) denote generalized Fibonacci and Lucas sequences defined by U₀=0,U₁=1; V₀=2,V₁=P, and U_{n+1}=PU_{n}-U_{n-1}, V_{n+1}=PV_{n}-V_{n-1} for n≥1. The purpose of this study, assuming P is odd, is to determine the values of n such that V_{n}=5□ and U_{n}=5□. Moreover, we solve the equations V_{n}=5V_{m}□ and U_{n}=5U_{m}□.
Vol. 16 (2015), No. 2, pp. 925-938
DOI: 10.18514/MMN.2015.1328