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A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers

Author

Listed:
  • Ana Paula Chaves

    (Instituto de Matemática e estatística, Universidade federal de Goiás, Goiás 74690-900, Brazil)

  • Pavel Trojovský

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic)

Abstract

The sequence of the k -generalized Fibonacci numbers ( F n ( k ) ) n is defined by the recurrence F n ( k ) = ∑ j = 1 k F n − j ( k ) beginning with the k terms 0 , … , 0 , 1 . In this paper, we shall solve the Diophantine equation F n ( k ) = ( F m ( l ) ) 2 + 1 , in positive integers m , n , k and l .

Suggested Citation

  • Ana Paula Chaves & Pavel Trojovský, 2020. "A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers," Mathematics, MDPI, vol. 8(6), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1010-:d:374091
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    References listed on IDEAS

    as
    1. Pavel Trojovský, 2019. "On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
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