Let $P(z)={\sum }_{1\le k\le n}{a}_k{z}^k$ for some $a_k\in \mathbb{C}$ with $|a_k|=1$ for $1\le k\le n$. Does there exist a constant $c>0$ such that, for $n\ge 2$, we have$$\underset{|z|=1}{\max }|P(z)|\ge (1+c)\sqrt{n}?$$