TY - JOUR

T1 - A polynomial variant of diophantine triples in linear recurrences

AU - Fuchs, Clemens

AU - Heintze, Sebastian

N1 - Funding Information:
Supported by Austrian Science Fund (FWF): I4406.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Diophantine triples

KW - Function fields

KW - Linear recurrence sequences

UR - http://www.scopus.com/inward/record.url?scp=85129164041&partnerID=8YFLogxK

U2 - 10.1007/s10998-022-00460-y

DO - 10.1007/s10998-022-00460-y

M3 - Article

AN - SCOPUS:85129164041

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

SN - 0031-5303

ER -