Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Problem 100

Statement. Let $A$ be a set of $n$ points in $\mathbb{R}^2$ such that all pairwise distances are at least $1$ and if two distinct distances differ then they differ by at least $1$ . Is the diameter of $A$ $\gg n$ ?

Status. Open.

Source. erdosproblems.com/100, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #100, https://www.erdosproblems.com/100.

References.

[GuKa15] Guth, Larry and Katz, Nets Hawk, On the Erdős distinct distances problem in the plane. Ann. of Math. (2) (2015), 155-190.

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

Linked from (3)

Distance Problems On the Erdős distinct distance problem in the plane Theorem 1.1 (p. 155): N points in the plane determine ≳ N/log N distinct distances

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