On the $X$-coordinates of Pell equations which are Tribonacci numbers
Volume 179 / 2017
Acta Arithmetica 179 (2017), 25-35
MSC: 11B39, 11J86.
DOI: 10.4064/aa8553-2-2017
Published online: 26 May 2017
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.
