Erdős problem 539 · problems.science

For $|A| = n$ , how small can the cofactor set $Q(A) = \{a / \gcd(a,b) : a, b \in A\}$ be? The answer is $h(n) = n^{1/2 + o(1)}$ : a new upper bound $h(n) \le n^{1/2} \exp(O(\sqrt{\log n}))$ matches the classical lower bound.

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9 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

539.lean

Retained formal statement2 of 8

To prove erdos_539.variants.sq it suffices to show $h(n)\ll n^{1/2}$ .

FormalConjectures/ErdosProblems/539.leanErdos539.erdos_539.variants.isBigO_sq1 lineExact file

1(fun n => ↑(Erdos539.cofactorThreshold n)) =O[Filter.atTop] fun n => √↑n

OpenStatement only, no proof

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