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
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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

  1. Ait-Amrane, L., & Behloul, D. (2017). On some Diophantine equations involving generalized Fibonacci and Lucas numbers, Colloq. Math., 150(2), 257–268.
  2. 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.
  3. 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.
  4. Keskin, R. (2014). Three identities concerning Fibonacci and Lucas numbers, Notes on Number Theory and Discrete Mathematics, 20 (5), 44–48.
  5. Lucas, E. (1878). Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math., 1, 184–240, 289–321.
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  7. Ribenboim, P. (2000). My Numbers, My Friends. Popular Lectures on Number Theory. Springer-Verlag, New York.

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Cite this paper

APA

Ait-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.

Chicago

Ait-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.

MLA

Ait-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.

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