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Decomposable polynomials in second order linear recurrence sequences

  • Clemens Fuchs
  • Christina Karolus
  • Dijana Kreso
Open Access
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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 \(\deg g,\deg h>1\). Under certain assumptions, and provided that h is not of particular type, we show that \(\deg g\) may be bounded by a constant independent of n, depending only on the sequence.

Mathematics Subject Classification

11B37 11R09 12E99 39B12 

Notes

Acknowledgements

Open access funding provided by Austrian Science Fund (FWF). The work on this manuscript was supported by FWF (Austrian Science Fund) Grant No. P24574 and No. J3955.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.University of SalzburgSalzburgAustria
  2. 2.Graz University of TechnologyGrazAustria

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