Some \(k\)-Fibonacci and \(k\)-Lucas identities by a matrix approach with applications. (English) Zbl 1511.11021

Summary: In this research, we study and find some identities involving \(k\)-Fibonacci and \(k\)-Lucas numbers by using a matrix approach. As an application of these identities we then obtain the solutions of some Diophantine equations.


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11D09 Quadratic and bilinear Diophantine equations


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