Erdős Problem 33
Let A ⊆ ℕ be a set such that every integer can be written as n^2 + a for some a in A and n ≥ 0. What is the smallest possible value of lim sup n → ∞ |A ∩ {1, …, N}| / N^(1/2)?
Mathematical statement
Let A ⊆ ℕ be a set such that every integer can be written as n^2 + a
for some a in A and n ≥ 0. What is the smallest possible value of
lim sup n → ∞ |A ∩ {1, …, N}| / N^(1/2)?
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_33
theorem erdos_33 : ⨅ A : {A : Set ℕ | AdditiveBasisCondition A}, Filter.atTop.limsup (fun N => (A.1 ∩ Icc 1 N).ncard / (√N : EReal)) = answer(sorry) := 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