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erdos_307_coprime_one_notMem

Specification

There are no examples known of the weakened coprime version if we insist that $1\not\in P\cup Q$.

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Lean 4 Statement 
theorem erdos_307_coprime_one_notMem : answer(sorry) ↔ ∃ P Q : Finset ℕ, 0 ∉ P ∩ Q ∧ 1 ∉ P ∪ Q ∧
    1 < #P ∧ 1 < #Q ∧ Set.Pairwise P Nat.Coprime ∧ Set.Pairwise Q Nat.Coprime ∧
    1 = (∑ p ∈ P, (p : ℚ)⁻¹) * (∑ q ∈ Q, (q : ℚ)⁻¹)
ID: ErdosProblems__307__erdos_307_coprime_one_notMem
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