Corpus ID: 219966663

A Polynomial Variant of Diophantine Triples in Linear Recurrences

@inproceedings{Fuchs2020APV,
  title={A Polynomial Variant of Diophantine Triples in Linear Recurrences},
  author={Clemens Fuchs and Sebastian Heintze},
  year={2020}
}
  • Clemens Fuchs, Sebastian Heintze
  • Published 2020
  • Mathematics
  • Let (Gn)∞n=0 be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation Gn = f1αn1 + · · ·+ fkα n k and polynomial characteristic roots α1, . . . , αk. For a fixed polynomial p, we consider triples (a, b, c) of pairwise distinct 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 triples if neither f1 nor f1α1 is a… CONTINUE READING