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Erdős problem 330

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

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/330.lean

Formal Conjectures

FormalConjectures/ErdosProblems/330.leanErdos330.erdos_330_statement4 linesExact file
True ↔  ∃ A h,    Erdos330.MinAsymptoticAddBasisOfOrder A h ∧      0 < A.upperDensity ∧ ∀ n ∈ A, 0 < (Erdos330.UnrepWithout A n h).upperDensity
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:330

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • Formalization

    Erdős AI contributions wiki · 5 May, 2026

    Machine
    Codex, GPT-5.5 Pro
    Open the source record

  • AI collaborating with humans

    Erdős AI contributions wiki · 24 Apr, 2026

    Machine
    GPT-5.5 Pro
    People
    David Turturean
    Open the source record

  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    David Turturean
    Reported outcome
    resolved
    Open the source record

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