The board / number theory / #677
Erdős Problem #677
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).
Denote by \(M(n, k)\) the least common multiple of the finite set \(\{n+1, \dotsc, n+k\}\). Is it true that for all \(m \geq n + k\), we get \(M(m, k) \neq M(n, k)\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/677.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/677
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k=2, k=3, and k=4 are fully closed, each independently verified — k=4 cross-checked against a real 1975 paper. k=6's overlapping case is now fully classified too (verified by independent brute force), reduced to four explicit curves for the hard disjoint case — honestly not yet closed, but the exact remaining computation is now specified.
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