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erdos_402

Specification

Prove that, for any finite set $A\subset\mathbb{N}$, there exist $a, b\in A$ such that $$ \gcd(a, b)\leq a/|A|. $$

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Lean 4 Statement 
theorem erdos_402 (A : Finset ℕ) (h₁ : 0 ∉ A) (h₂ : A.Nonempty) : ∃ᵉ (a ∈ A) (b ∈ A),
    a.gcd b ≤ (a / A.card : ℚ)
ID: ErdosProblems__402__erdos_402
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