On decompositions of binary recurrent polynomials

Research output: Contribution to journalArticlepeer-review

Abstract

Polynomial decomposition expresses a polynomial f as the functional composition f= g∘ h of lower degree polynomials g and h, and has various applications. In this paper, we will show that for a minimal, non-degenerate, simple, binary, linearly recurrent sequence (Gn(x))n=0∞ of complex polynomials whose coefficients in the Binet form are constants, if G n(x) = g(h(x)) , then apart from some exceptional situations that have to be taken into account, the degree of g is bounded by a constant independent of n. We will build on a general but conditional result of this type that already exists in the literature. We will then present one Diophantine application of the main result.

Original languageEnglish
Article number458
Pages (from-to)135-148
Number of pages14
JournalMonatshefte für Mathematik
Volume199
Issue number1
DOIs
Publication statusPublished - Sep 2022

Keywords

  • polynomial decomposition
  • Linear recurrences
  • Diophantine equations
  • Polynomial decomposition

ASJC Scopus subject areas

  • Mathematics(all)

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