The board / number theory / #389
Erdős Problem #389
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).
Is it true that for every \(n \geq 1\) there is a \(k\) such that \[ n(n + 1) \cdots (n + k - 1) \mid (n + k) \cdots (n + 2k - 1)? \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/389.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA375071
Original pageerdosproblems.com/389
Attempts
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Erdős #389 itself stays open. Our shift conjecture got refuted by an exact counterexample — then a same-day follow-up proved an exact obstruction formula and certified a 14th minimal witness (n=28), piggybacking on a public exhaustive computation for a different Erdős problem.
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