Positive integer solutions of the diophantine equation x(2)-L(n)xy +(-1)(n)y(2) = +/- 5(r)

Abstract

In this paper, we consider the equation x (2)-L (n) x y+(-1) (n) y (2) = +/- 5 (r) and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions of the equation x (2)-L (n) x y+(-1) (n) y (2) = +/- 5 (r) when the equation has positive integer solutions.