Question 6
(CUB) Let $P(z)$ and $Q(z)$ be complex-variable polynomials, with degree not less than 1. Let
$$P_k=\{z\in\mathbb C\mid P(z)=k\},\qquad Q_k=\{z\in\mathbb C\mid Q(z)=k\}.$$
Let also $P_0=Q_0$ and $P_1=Q_1$. Prove that $P(z)\equiv Q(z)$.
$$P_k=\{z\in\mathbb C\mid P(z)=k\},\qquad Q_k=\{z\in\mathbb C\mid Q(z)=k\}.$$
Let also $P_0=Q_0$ and $P_1=Q_1$. Prove that $P(z)\equiv Q(z)$.