Abstract

We study the problem of finding all integer solutions of the Diophantine equations x^{2} − 5F_{n}xy − 5 (−1)^{n} y^{2} = ±L_{n}^{2}, x^{2} − L_{n}xy + (−1)^{n} y^{2} = ±5F_{n}^{2}, and x^{2}−L_{n}xy+(−1)^{n} y^{2} = ±F_{n}^{2}. Using these equations, we also explore all integer solutions of some other Diophantine equations.