MMN-568
Positive integer solutions of the diophantine equations $x^2 -5 F_n xy - 5(-1)^n y^2 = \pm 5^r$
Abstract
In this study, we consider the Diophantine equations given in the title and determine
when these equations have positive integer solutions. Moreover, we find all positive integer
solutions of them in terms of Fibonacci and Lucas numbers.
Vol. 14 (2013), No. 3, pp. 959-972
DOI: 10.18514/MMN.2013.568