MathDB

Let

p(x)

be a polynomial with integer coefficients and let

n

be an integer. Suppose that there is a positive integer

k

for which

f^{(k)}(n) = n

, where

f^{(k)}(x)

is the polynomial obtained as the composition of

k

polynomials

f

. Prove that

p(p(n)) = n

Problem Statement