Source authenticated
Erdős Problem #953
What is the largest possible measure of a subset of a radius-$R$ disk in $\mathbb{R}^2$ containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives $M(R) \ll R^{1/2}$; with Sárközy's lower construction, $M(R) = R^{1/2 + o(1)}$.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Apr 27, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Erdős Problem #953 · Erdős #953 · Problem 953
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Lineage and corrections
This event attributed to GPT-5.5 Pro