Question 25
For any positive integer $k$, denote the sum of digits of $k$ in its decimal representation by $S(k)$. Find all polynomials $P(x)$ with integer coefficients such that for any positive integer $n \geqslant 2016$, the integer $P(n)$ is positive and
$$
S(P(n))=P(S(n))
$$
$$
S(P(n))=P(S(n))
$$