The board / number theory / #47
Erdős Problem #47
PROVED LEANdatabase updated 2025-11-28
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(\delta>0\) and \(N\) is sufficiently large in terms of \(\delta\), and \(A\subseteq\{1,\ldots,N\}\) is such that \(\sum_{a\in A}\frac{1}{a}>\delta \log N\) then must there exist \(S\subseteq A\) such that \(\sum_{n\in S}\frac{1}{n}=1\)? Bloom [Bl21] proved this in the affirmative.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/47.Prize$100
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/47
Attempts
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