The board / number theory / #286
Erdős Problem #286
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).
Let \(k\geq 2\). Is it true that there exists an interval \(I\) of width \((e-1+o(1))k\) and integers \(n_1<\cdots<n_k\in I\) such that \[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\] The answer is yes, proved by Croot [Cr01].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/286.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/286
Attempts
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