The board / number theory / #1210
Erdős Problem #1210
OPENdatabase updated 2026-04-04
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(A\subseteq [1,n)\) be a set of integers such that \((a,b)=1\) for all distinct \(a,b\in A\). Is it true that \(\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)\)?
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/1210.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1210
Attempts
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Exact radical-support compression proved and a from-scratch rational verifier certifies the sharp bound \(M(n)\leq\sum_{p<n}1/p+1\) for every \(2\leq n\leq1000\); the uniform problem remains blocked b
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