On the $x$-coordinates of Pell equations which are Fibonacci numbers II
Volume 149 / 2017
Colloquium Mathematicum 149 (2017), 75-85
MSC: 11A25 11B39, 11J86.
DOI: 10.4064/cm6960-8-2016
Published online: 20 April 2017
Abstract
For an integer $d\geq 2$ which is not a square, we show that there is at most one positive integer $x$ appearing in a solution of the Pell equation $x^2-dy^2=\pm 4$ which is a Fibonacci number, except when $d=2, 5$, where we have exactly two values of $x$ being members of the Fibonacci sequence.
