Erdős Problem #91
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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A set \(A\) is 'optimal' if it has \(n\) points and achieves the minimum distance count.
Two finite sets of points in \(\mathbb{R}^2\) are similar if one can be mapped to the other by a DilationEquiv.
Equilateral triangle with unit side length, resting on the x-axis with one vertex at the origin.
Suppose \(A\subset \mathbb{R}^2\) has \(\lvert A\rvert=n\) and minimises the number of distinct distances between points in \(A\). Prove that for large \(n\) there are at least two (and probably many) such \(A\) which are non-similar.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 7 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/91.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA186704
Original pageerdosproblems.com/91
Attempts
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