The board / number theory / #402
Erdős Problem #402
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Prove that, for any finite set \(A\subset\mathbb{N}\), there exist \(a, b\in A\) such that \[ \gcd(a, b)\leq a/|A|. \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/402.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/402
Attempts
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