All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 330

Does there exist a minimal basis ANA \subset \mathbb{N} with positive density such that, for any nAn \in A, the (upper) density of integers which cannot be represented without using nn is positive?

Mathematical statement

Does there exist a minimal basis ANA \subset \mathbb{N} with positive density such that, for any nAn \in A, the (upper) density of integers which cannot be represented without using nn is positive?

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_330_statement

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_330_statement :    answer(sorry)   (A : Set ),  h, MinAsymptoticAddBasisOfOrder A h  A.HasPosDensity      n  A, Set.HasPosDensity (UnrepWithout A n h) := 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