Let
be a non-constant polynomial with integer coefficients. Prove that there is no function
from the set of integers into the set of integers such that the number of integers
with
is equal to
for every
, where
denotes the
-fold application of
.
Proposed by Jozsef Pelikan, Hungary
%V0
Let $P\!\left(x\right)$ be a non-constant polynomial with integer coefficients. Prove that there is no function $T$ from the set of integers into the set of integers such that the number of integers $x$ with $T^n\!\left(x\right) = x$ is equal to $P\!\left(n\right)$ for every $n \geqslant 1$, where $T^n$ denotes the $n$-fold application of $T$.
Proposed by Jozsef Pelikan, Hungary
Školjka