MathDB

Find all polynomials

P

with integer coefficients such that

P (0)\ne 0

and

P^n(m)\cdot P^m(n)

is a square of an integer for all nonnegative integers

n, m

.
Remark: For a nonnegative integer

k

and an integer

n

P^k(n)

is defined as follows:

P^k(n) = n

k = 0

and

P^k(n)=P(P(^{k-1}(n))

k >0

.
Proposed by Adrian Beker.

Problem Statement