Larger families of solutions to some Diophantine equations

Lyes Ait-Amrane
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 25–31
DOI: 10.7546/nntdm.2019.25.1.25-31
Full paper (PDF, 138 Kb)

Details

Authors and affiliations

Lyes Ait-Amrane
USTHB, Faculty of Mathematics, LATN Laboratory,
BP 32, El Alia, 16111, Bab Ezzouar, Algiers, Algeria
Ecole nationale Supérieure d’Informatique (ESI)
BP 68M Oued Smar, 16270, El Harrach, Algiers, Algeria

Abstract

In this paper, we give three identities involving the Lucas sequences of the first kind and of the second kind in order to obtain infinite families of solutions to some Diophantine equations. Some of these families are new and the others are larger than those known until now.

Keywords

• Fibonacci and Lucas numbers
• Lucas sequences
• Diophantine equations

2010 Mathematics Subject Classification

• 11B37
• 11B39
• 11D45
• 40C05

References

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