Let
be a polynomial of degree
with integer coefficients and let
be a positive integer. Consider the polynomial
, where
occurs
times. Prove that there are at most
integers
such that
.
%V0
Let $P(x)$ be a polynomial of degree $n > 1$ with integer coefficients and let $k$ be a positive integer. Consider the polynomial $Q(x) = P(P(\ldots P(P(x)) \ldots ))$, where $P$ occurs $k$ times. Prove that there are at most $n$ integers $t$ such that $Q(t) = t$.
Školjka