Erdős Problem #94
PROVED LEANdatabase updated 2026-01-15
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).
The regular \(n\)-gon inscribed in the unit circle.
Suppose \(n\) points in \(\mathbb{R}^2\) determine a convex polygon and the set of distances between them is \(\{u_1,\ldots,u_t\}\). Suppose \(u_i\) appears as the distance between \(f(u_i)\) many pairs of points. Then \[\sum_i f(u_i)^2 \ll n^3.\] In [Er97c] Erdős claims that Fishburn solved this, but gives no reference.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/94.Prize£25
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA387858
Original pageerdosproblems.com/94
Attempts
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