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erdos_940.variants.three_cubes

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Is it true that the set of integers which are the sum of at most three cubes has density $0$?

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Lean 4 Statement 
theorem erdos_940.variants.three_cubes :
    answer(sorry) ↔
    {n : ℕ | ∃ (S : Multiset ℕ), S.card ≤ 3 ∧ n = (Multiset.map (· ^ 3) S).sum}.HasDensity 0
ID: ErdosProblems__940__erdos_940.variants.three_cubes
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