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arXiv · 1703.03258

Decomposable polynomials in second order linear recurrence sequences

Clemens Fuchs·Christina Karolus·Dijana Kreso
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Abstract

We study elements of second order linear recurrence sequences $(G_n)_{n= 0}^{\infty}$ of polynomials in $\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\circ h$ for some $g, h\in \mathbb{C}[x]$ satisfying $\operatorname{deg}g,\operatorname{deg}h>1$. Under certain assumptions, and provided that $h$ is not of particular type, we show that $\operatorname{deg}g$ may be bounded by a constant independent of $n$, depending only on the sequence.

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Clemens Fuchs, Christina Karolus, Dijana Kreso. 2017-03-09. Decomposable polynomials in second order linear recurrence sequences. https://arxiv.org/abs/1703.03258

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