SCHWEITZER 2017 Problem 5

For every non-constant polynomial $p$ , let $H_p=\big\{z\in \mathbb{C} \big| |p(z)|=1\big\}$ . Prove that if $H_p=H_q$ for some polynomials $p,q$ , then there exists a polynomial $r$ such that $p=r^m$ and $q=\xi\cdot r^n$ for some positive integers $m,n$ and constant $|\xi|=1$ .