Abstract
AbstractPolynomial decomposition expresses a polynomial f as the functional composition $$f=g\circ h$$
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 $$(G_n(x))_{n=0}^\infty $$
(
G
n
(
x
)
)
n
=
0
∞
of complex polynomials whose coefficients in the Binet form are constants, if $$G_n(x)=g(h(x))$$
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.
Publisher
Springer Science and Business Media LLC