The board / primitive sets / #143
Erdős Problem #143
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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Let \(A \subseteq (1, \infty)\) be a countably infinite set such that for all \(x\neq y\in A\) and integers \(k \geq 1\) we have \(|kx - y| \geq 1\).
Does this imply that \[ \liminf \frac{|A \cap [1,x]|}{x} = 0? \]
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/143.Prize$500
Topicsprimitive sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/143
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