Notes on Number Theory and Discrete Mathematics
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Volume 27, 2021, Number 4, Pages 62—79
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Using the explicit formulas of the generating polynomials of Fibonacci and Lucas, we prove some new identities involving Fibonacci and Lucas numbers. As an application of these identities, we show how some Diophantine equations have infinitely many solutions. To illustrate the powerful of this elementary method, we give proofs of many known formulas.
- Fibonacci number
- Lucas number
- Diophantine equation
2020 Mathematics Subject Classification
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Cite this paper
Benoumhani, M. (2021). An elementary unified approach to prove some identities involving Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 27(4), 62-79, doi: 10.7546/nntdm.2021.27.4.62-79.