Erdős Problem #93
PROVED LEANdatabase updated 2025-02-17
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(n\) distinct points in \(\mathbb{R}^2\) form a convex polygon then they determine at least \(\lfloor \frac{n}{2}\rfloor\) distinct distances. Solved by Altman [Al63].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/93.Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.