On the $X$-coordinates of Pell equations which are Tribonacci numbers

Florian Luca; Amanda Montejano; Laszlo Szalay; Alain Togbé

On the $X$-coordinates of Pell equations which are Tribonacci numbers

Number Theory 2017-01-02 v1

Authors: Florian Luca , Amanda Montejano , Laszlo Szalay , Alain Togbé

Abstract

For an integer $d\geq 2$ which is not a square, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=\pm 1$ which is a Tribonacci number, with a few exceptions that we completely characterize.

Keywords

Pell equations Tribonacci numbers Diophantine equations number theory

Cite

@article{arxiv.1612.09546,
  title  = {On the $X$-coordinates of Pell equations which are Tribonacci numbers},
  author = {Florian Luca and Amanda Montejano and Laszlo Szalay and Alain Togbé},
  journal= {arXiv preprint arXiv:1612.09546},
  year   = {2017}
}

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10 pages

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