The board / number theory / #299
Erdős Problem #299
DISPROVED LEANdatabase updated 2025-12-29
The statement as posed is false. 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).
Is there an infinite sequence \(a_1 < a_2 < \dots\) such that \(a_{i+1} - a_i = O(1)\) and no finite sum of \(\frac{1}{a_i}\) is equal to 1? There does not exist such a sequence, which follows from the positive solution to [erdosproblems.com/298] by Bloom [Bl21]. This was formalized in Lean 3 by Bloom and Mehta.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/299.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/299
Attempts
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