erdos_885

Is it true that, for every $k \geq 1$, there exist integers $N_1 < \dots < N_k$ such that $|\cap_i D(N_i)| \geq k$?

theorem erdos_885 : answer(sorry) ↔ ∀ k ≥ 1,
    ∃ Ns : Finset ℕ,
      (∀ n ∈ Ns, 1 ≤ n) ∧
      Ns.card = k ∧
      (⋂ n ∈ Ns, factorDifferenceSet n).ncard ≥ k

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