Solutions of Some Diophantine Equations Using Generalized Fibonacci and Lucas Sequences

Abstract

In this study, we deal with some Diophantine equations. By using the generalized Fibonacci and Lucas sequences, we obtain all integer solutions of some Diophantine equations such as x(2) - kxy - y(2) = -/+ 1, x(2) - kxy + y(2) = 1, x(2) - kxy - y(2) = -/+(k(2) + 4), x(2) - (k(2) + 4)xy + (k(2) + 4)y(2) = -/+ k(2), x(2) - kxy + y(2) = -(k(2) - 4), and x(2) - (k(2) - 4)xy - (k(2) - 4)y(2) = k(2). Some of the results are known but we think that our proofs are new and different from the others.