Erdős Problem 256

### What is the conjecture

https://www.erdosproblems.com/256

Let $n\geq 1$ and $f(n)$ be maximal such that, for every $a_1\leq \cdots \leq a_n\in \mathbb{N}$ we have

$$\max_{\lvert z\rvert=1}\left\lvert \prod_{i}(1-z^{a_i})\right\rvert\geq f(n).$$

Estimate $f(n)$ - in particular, is it true that there exists some constant $c>0$ such that
$$f(n) \geq \exp(n^{c})?$$

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else