Erdős Problem 1045

### What is the conjecture

https://www.erdosproblems.com/1045

Let $z_1,\ldots,z_n\in \mathbb{C}$ with $\lvert z_i-z_j\rvert\leq 2$ for all $i,j$, and
$$\Delta(z_1,\ldots,z_n)=\prod_{i\neq j}\lvert z_i-z_j\rvert.$$
What is the maximum possible value of $\Delta$? Is it maximised by taking the $z_i$ to be the vertices of a regular polygon?

Status: falsifiable

### 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

Start by reading the Erdős Problems 1045 conjecture at https://www.erdosproblems.com/1045 and inspecting this repository's existing formalized conjectures for the relevant conventions. Done means the conjecture is added to the Lean collection with a statement matching the linked problem.

Written by the indexing model from the issue text.