The board / number theory / #285
Erdős Problem #285
PROVED LEANdatabase updated 2026-08-23
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).
Let \(f(k)\) be the minimal value of \(n_k\) such that there exist \(n_1 < n_2 < \dots < n_k\) with \[ 1 = \frac{1}{n_1} + \cdots + \frac{1}{n_k}. \] Is it true that \[ f(k) = (1 + o(1)) \frac{e}{e - 1} k ? \] Proved by Martin [Ma00]. [Ma00] Martin, Greg, _Denser Egyptian fractions_. Acta Arith. (2000), 231-260.
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/285.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA030659
Original pageerdosproblems.com/285
Attempts
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