Decomposable polynomials in second order linear recurrence sequences
Clemens Fuchs, Christina Karolus, Dijana Kreso · manuscripta mathematica · 2018
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.