Moussa Benoumhani

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 62—79

DOI: 10.7546/nntdm.2021.27.4.62-79

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## Details

### Authors and affiliations

Moussa Benoumhani

*Department of Mathematics, University of Msila
Msila, Algeria
*

### Abstract

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.

### Keywords

- Fibonacci number
- Lucas number
- Polynomials
- Diophantine equation

### 2020 Mathematics Subject Classification

- 11B39
- 11B65

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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.