erdos_56

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? To avoid trivial counterexamples, we must insist that $N$ be at least the $k$th prime.

theorem erdos_56 : (∀ᵉ (k > 0) (N ≥ (k-1).nth Nat.Prime),
    (MaxWeaklyDivisible N k = (FirstPrimesMultiples N k).card)) ↔
    answer(False)

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