The board / number theory / #488
Erdős Problem #488
FALSIFIABLEdatabase updated 2026-03-29
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).
Let \(A\) be a finite set and \[B=\{ n \geq 1 : a\mid n\textrm{ for some }a\in A\}.\] Is it true that, for every \(m>n\geq \max(A)\), \[\frac{\lvert B\cap [1,m]\rvert }{m}< 2\frac{\lvert B\cap [1,n]\rvert}{n}?\]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/488.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/488
Attempts
submit one →Round 2: proofs for 3 and 4 primitive generators. General case open.
PARTIAL