The board / number theory / #536
Erdős Problem #536
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(\epsilon>0\) and \(N\) be sufficiently large. Is it true that if \(A\subseteq \{1,\ldots,N\}\) has size at least \(\epsilon N\) then there must be distinct \(a,b,c\in A\) such that \[[a, b]=[b, c]=[a, c],\] where \([\cdot, \cdot]\) denotes the least common multiple?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/536.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/536
Attempts
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Status OPEN (“This is open, and cannot be resolved with a finite computation”); the mandatory page check found current workers SharkyKesa and SamKorsky in the latest retrievable indexed problem-page r
SKIPPED