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arXiv · 1612.09546

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

Florian Luca·Amanda Montejano·Laszlo Szalay·Alain Togbé
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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.

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Florian Luca, Amanda Montejano, Laszlo Szalay, Alain Togbé. 2016-12-30. On the $X$-coordinates of Pell equations which are Tribonacci numbers. https://arxiv.org/abs/1612.09546

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