Let $N \geq p_{k}$ where $p_{k}$ is the $k$ th prime. Suppose $A \subseteq {1, \dots, N}$ is such that there are no $k + 1$ elements of $A$ which are relatively prime. An example is the set of all multiples of the first $k$ primes. Is this the largest such set?

Worked, still open.

number theory · solved · prize $10 · formalized (Lean) · 0 attempts

machinery: extremal-set-system,intersecting-family,AK-pushing-pulling,prime-distribution,covering-system

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · api (literature)

lemma weaklyDivisible_empty (k : ℕ): WeaklyDivisible k {}

solved