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

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## 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

- Ait-Amrane, L., & Behloul, D. (2017). On some Diophantine equations involving generalized Fibonacci and Lucas numbers, Colloq. Math., 150(2), 257–268.
- Andreescu, T., & Andrica, D. (2014). Equations with solution in terms of Fibonacci and Lucas sequences, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 22 (3), 5–12.
- Demirtürk, B. & Keskin, R. (2009). Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers, J. Integer Seq., 12(8), Article 09.8.7, 14 pp.
- Keskin, R. (2014). Three identities concerning Fibonacci and Lucas numbers, Notes on Number Theory and Discrete Mathematics, 20 (5), 44–48.
- Lucas, E. (1878). Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math., 1, 184–240, 289–321.
- Ribenboim, P. (1996). The New Book of Prime Number Records, Springer-Verlag, New York.
- Ribenboim, P. (2000). My Numbers, My Friends. Popular Lectures on Number Theory. Springer-Verlag, New York.

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## Cite this paper

APAAit-Amrane, L. (2019). Larger families of solutions to some Diophantine equations. Notes on Number Theory and Discrete Mathematics, 25(1), 25-31, doi: 10.7546/nntdm.2019.25.1.25-31.

ChicagoAit-Amrane, Lyes. “Larger Families of Solutions to Some Diophantine Equations.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 25-31, doi: 10.7546/nntdm.2019.25.1.25-31.

MLAAit-Amrane, Lyes. “Larger Families of Solutions to Some Diophantine Equations.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 25-31. Print, doi: 10.7546/nntdm.2019.25.1.25-31.