Question 9
Find all polynomials $P(x)$ with integer coefficients such that there exists a positive integer $N$ such that for all positive integers $n \gt N$ we have $P(n) \gt 0$ and
$$
n + P(n) \mid n^{P(n)} + P(n)^n.
$$
$$
n + P(n) \mid n^{P(n)} + P(n)^n.
$$