Find all positive integers $n$ for which the following statement holds: For any two polynomials $P(x)$ and $Q(x)$ of degree $n$ there exist monomials $ax^k$ and $bx^{ell}, 0 \le k,\ ell \le n$, such that the graphs of $P(x) + ax^k$ and $Q(x) + bx^{ell}$ have no common points.