Erdős problem 888 · problems.science

What is the size of the largest $A\subseteq \{1,\ldots,n\}$ such that if $a\leq b\leq c\leq d\in A$ are such that $abcd$ is a square then $ad=bc$ ?

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

888.lean

Retained formal statement4 of 4

Cambie and Weisenberg have noted in the comments that the set of semiprimes also works, showing $(1+o(1))\frac{\log\log n}{\log n}n \leq \lvert A\rvert$ is achievable.

FormalConjectures/ErdosProblems/888.leanErdos888.erdos_888.variants.semiprimes1 lineExact file

1(fun n => ↑n * Real.log (Real.log ↑n) / Real.log ↑n) =O[Filter.atTop] fun n => ↑(Nat.findGreatest (Erdos888.p n) n)

SolvedStatement only, no proof

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