Three identities concerning Fibonacci and Lucas numbers

Refik Keskin
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 5, Pages 44—48
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Authors and affiliations

Refik Keskin
Department of Mathematics, Faculty of Arts and Science
Sakarya University, Turkey

Abstract

In the literature, there are many identities about Fibonacci and Lucas numbers. In this study, we give three identities concerning Fibonacci and Lucas numbers. Then we present some Diophantine equations such as z2 + x2 + y2 = xyz + 4.

Keywords

  • Fibonacci numbers
  • Lucas numbers
  • Fibonacci matrix
  • Diophantine equation

AMS Classification

  • 11B37
  • 11B39
  • 40C05

References

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  4. Keskin, R., Solutions of Some Quadratics Diophantine Equations, Computers and Mathe- matics with Applications , Vol. 60, 2010, 2225–2230.
  5. Keskin, R., B. Demirtürk, Some new Fibonacci and Lucas identities by matrix methods, Internat. J. Math. Ed. Sci. Tech. , Vol. 41, 2010, No. 3, 379–387.
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  8. Vajda, S., Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Limited Publ., England, 1989.
  9. Related papers

    Cite this paper

    APA

    Keskin, R. (2014). Three identities concerning Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 20(5), 44-48.

    Chicago

    Keskin, Refik. “Three Identities Concerning Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 44-48.

    MLA

    Keskin, Refik. “Three Identities Concerning Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 44-48. Print.

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