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.

Sources

Browse retained paths and inspect the exact material available for this Problem.

9 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

539.lean

Retained formal statement7 of 8

To prove erdos_539.variants.sq_cube_root it suffices to show $n^{2/3}\ll h(n)$ .

FormalConjectures/ErdosProblems/539.leanErdos539.erdos_539.variants.sq_cube_root_isBigO1 lineExact file

1(fun n => ↑n ^ (2 / 3)) =O[Filter.atTop] fun n => ↑(Erdos539.cofactorThreshold n)

OpenStatement only, no proof

Sources

Search problems.science