Diophantine Equations Related with Linear Binary Recurrences

Abstract

. In this paper we find all solutions of four kinds of the Diophantine equations x 2 ± V t xy − y 2 ± x = 0 and x 2 ± V t xy − y 2 ± y = 0 , for an odd number t , and, x 2 ± V t xy + y 2 − x = 0 and x 2 ± V t xy + y 2 − y = 0 , for an even number t , where V n is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.