An elementary unified approach to prove some identities involving Fibonacci and Lucas numbers

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
Full paper (PDF, 236 Kb)

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

References

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