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arXiv · 2401.06537

Twisted rational zeros of linear recurrence sequences

Yuri Bilu·Florian Luca·Joris Nieuwveld·Joël Ouaknine·James Worrell
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Abstract

We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that $1/3$ and $-5/3$ are the only twisted rational zeros which are not integral zeros.

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Yuri Bilu, Florian Luca, Joris Nieuwveld, Joël Ouaknine, James Worrell. 2024-01-12. Twisted rational zeros of linear recurrence sequences. https://arxiv.org/abs/2401.06537

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