Erdős Problem 41
Let A ⊆ ℕ be an infinite set such that the triple sums a + b + c are all distinct for a, b, c in A (aside from the trivial coincidences). Is it true that liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0?
Mathematical statement
Let A ⊆ ℕ be an infinite set such that the triple sums a + b + c are all distinct for
a, b, c in A (aside from the trivial coincidences). Is it true that
liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0?
Statement source: Erdős Problems statement material
Statement terms: Source-specific
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Statement artifacts, not proofs
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Pinned Lean formulation 1
erdos_41
theorem erdos_41 (A : Set ℕ) (h_triple : NtupleCondition A 3) (h_infinite : A.Infinite) : Filter.atTop.liminf (fun N => (A ∩ Icc 1 N).ncard / (N : ℝ)^(1/3 : ℝ)) = 0 := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References