Erdős Problem #98
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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\(h(n)\) is the minimum number of distinct distances determined by any \(n\)-point set in \(\mathbb{R}^2\) in general position (no three collinear, no four cocyclic).
Let \(h(n)\) be such that any \(n\) points in \(\mathbb{R}^2\), with no three on a line and no four on a circle, determine at least \(h(n)\) distinct distances. Does \(h(n)/n\to \infty\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/98.Attempts
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