MathNet 2013 Question 65

Find all pairs $(m, n)$ of positive integers $m$ and $n$ such that for all polynomial $P(x)$ with real coefficients and $\deg P(x) = m$ there exists a polynomial $Q(x)$ with real coefficients and $\deg Q(x) = n$ such that $Q(P(x))$ is divisible by $Q(x)$.
(A. Mirotin, S. Mazanik, I. Voronovich)