A polynomial variant of diophantine triples in linear recurrences

Clemens Fuchs*, Sebastian Heintze

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let (Gn)n=0∞ be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation Gn=f1α1n+⋯+fkαkn and polynomial characteristic roots α1, … , αk. For a fixed polynomial p, we consider sets { a, b, c} consisting of three non-zero polynomials such that ab+ p, ac+ p, bc+ p are elements of (Gn)n=0∞. We will prove that under a suitable dominant root condition there are only finitely many such sets if neither f1 nor f1α1 is a perfect square.

Original languageEnglish
JournalPeriodica Mathematica Hungarica
Publication statusE-pub ahead of print - 2022


  • Diophantine triples
  • Function fields
  • Linear recurrence sequences

ASJC Scopus subject areas

  • Mathematics(all)


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