Erdős Problem 1087

### What is the conjecture

https://www.erdosproblems.com/1087

Let $f(n)$ be minimal such that every set of $n$ points in $\mathbb{R}^2$ contains at most $f(n)$ many sets of four points which are 'degenerate' in the sense that some pair are the same distance apart. Estimate $f(n)$ - in particular, is it true that $f(n)\leq n^{3+o(1)}$?

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

Start by reading the linked Erdős Problems 1087 statement and the repository’s existing formalized conjectures. The issue names no Lean file, test, or entry point, so the project’s conventions must be located first. Done means adding a formalized statement of this conjecture consistent with those conventions.

Written by the indexing model from the issue text.