Erdős Problem #1082
FALSIFIABLEdatabase updated 2025-10-17
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(A\subset \mathbb{R}^2\) be a set of \(n\) points with no three on a line. Does \(A\) determine at least \(\lfloor n/2\rfloor\) distinct distances?
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/1082.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1082
Attempts
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proved the conjectured exact value for all n<=15 (modulo the published g(k) classifications), proved D(A)>=ceil(n/3) modulo the planar diameter-graph theorem, and exactly ruled out the standard seven-
PARTIAL