MathDB

Let

P(x)

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(x)=x

is equal to

P(n)

for every

n\geq 1

, where

T^n

denotes the

n

-fold application of

T

.
Proposed by Jozsef Pelikan, Hungary

Problem Statement