On generalized Fibonacci quadratics

Neşe Ömür and Zehra Betül Gür
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 198—204
DOI: 10.7546/nntdm.2020.26.2.198-204
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Authors and affiliations

Neşe Ömür 
Department of Mathematics, University of Kocaeli
41380 Izmit Kocaeli, Turkey

Zehra Betül Gür
Department of Mathematics, University of Kocaeli
41380 Izmit Kocaeli, Turkey

Abstract

In this paper, we consider generalized Fibonacci quadratics and give solutions of them under certain conditions. For example, for odd number k, under condition n\!=\!U_{k}^{2}% \left(V_{k}V_{k(4n+1)}\!-\!4\right), the equation

    \begin{equation*} nx^{2}+\left( V_{k}n-2U_{k}^{2}D\right) x-\left( n+DU_{k}^{2}\left( V_{k}+2\right) \right) =0 \end{equation*}

has rational roots.

Keywords

  • Generalized Fibonacci numbers
  • Fibonacci quadratics
  • Pythagorean triplet

2010 Mathematics Subject Classification

  • 11B39
  • 11B50
  • 97F40

References

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Cite this paper

Ömür, N., & Betül Gür, Z. (2020). On generalized Fibonacci quadratics. Notes on Number Theory and Discrete Mathematics, 26 (2), 198-204, doi: 10.7546/nntdm.2020.26.2.198-204.

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