Erdős Problem 604

### What is the conjecture

https://www.erdosproblems.com/604

Given $n$ distinct points $A\subset\mathbb{R}^2$ must there be a point $x\in A$ such that
$$\\#\\{ d(x,y) : y \in A\\} \gg n^{1-o(1)}?$$
Or even $\gg n/\sqrt{\log n}$?

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