Decomposable polynomials in second order linear recurrence sequences

2017/03/09 by Fuchs, Clemens, Karolus, Christina, Kreso, Dijana · 1 citation
#11B37 (Primary) #11R09 #12E99 #39B12 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.03258

Abstract

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

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• Diophantine Equations for Polynomial Recursive Sequences

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