The board / number theory / #711
Erdős Problem #711
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There are distinct \(a_1,\ldots,a_n\) in the open interval \((m,m+L)\) such that \(i \mid a_i\) for every \(1 \leq i \leq n\).
\(L\) is the minimal interval length for the parameters \((n,m)\).
Let \(f(n,m)\) be minimal such that \((m,m+f(n,m))\) contains distinct integers \(a_1,\ldots,a_n\) with \(k \mid a_k\) for \(1 \leq k \leq n\). Prove that \(\max_m f(n,m) \leq n^{1+o(1)}\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/711.Prize₹1,000
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA390246
Original pageerdosproblems.com/711
Attempts
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Live page status is OPEN with 0 claimed proofs, but it lists “Currently working on this problem: skominers” (accessed 2026-07-27); the mandated collision rule therefore forbids an attempt.
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