Source labels openChecked July 26, 2026

Erdős Problem 749

Let $\epsilon>0$ . Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$ ?

Number theory AMS 11

Mathematical statement

Let $\epsilon>0$ . Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$ ?

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_749

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_749 : answer(sorry) ↔ ∀ ε > (0 : ℝ),    ∃ A : Set ℕ, 1 - ε ≤ lowerDensity (A + A) ∧    ((Nat.cast (R := ℝ) ∘ sumRep A) ≪ (fun n => (1: ℝ))) := 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/749background