The board / number theory / #287
Erdős Problem #287
FALSIFIABLEdatabase updated 2025-12-05
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The maximum gap between consecutive terms of a finite sequence `s : Fin k → ℕ`, i.e., \(\max_{0 \le i < k-1} (s(i+1) - s(i))\).
Let \(k\geq2\). Is it true that, for any distinct integers \(1 < n_1 < \cdots < n_k\) such that \(\sum_{i=1}^k \frac{1}{n_i} = 1\), we must have \(\max(n_{i+1} - n_i) \geq 3\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/287.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/287
Attempts
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Live page status on 2026-07-26 is FALSIFIABLE/open with 0 claimed proofs, but it lists stffp under “Currently working on this problem” (and “Interested in collaborating”); mandatory collision-avoidanc
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