1981 IMO 第 6 题

Let $P(z)$ and $Q(z)$ be complex-variable polynomials, with degree not less than 1. Let $$P_{k}=\{z \in \mathbb{C} \mid P(z)=k\}, \quad Q_{k}=\{z \in \mathbb{C} \mid Q(z)=k\}$$ Let also $P_{0}=Q_{0}$ and $P_{1}=Q_{1}$. Prove that $P(z) \equiv Q(z)$.

设 $P(z)$ 和 $Q(z)$ 为复变量多项式，次数不小于 1。设 $$P_{k}=\{z \in \mathbb{C} \mid P(z)=k\}, \quad Q_{k}=\{z \in \mathbb{C} \mid Q(z)=k\}$$ 还设 $P_{0}=Q_{0}$ 且$P_{1}=Q_{1}$。证明 $P(z) \equiv Q(z)$。