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Erdős problem 865

There exists a constant C>0C>0 such that, for all large NN, if A⊆{1,…,N}A\subseteq \{1,\ldots,N\} has size at least 58N+C\frac{5}{8}N+C then there are distinct a,b,c∈Aa,b,c\in A such that a+b,a+c,b+c∈Aa+b,a+c,b+c\in A.

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/865.lean

Formal Conjectures

FormalConjectures/ErdosProblems/865.leanErdos865.erdos_8654 linesExact file
∃ C > 0,  ∀ᶠ (N : ℕ) in Filter.atTop,    ∀ A ⊆ Finset.Icc 1 N,      ↑A.card ≥ 5 / 8 * ↑N + C → ∃ a ∈ A, ∃ b ∈ A, ∃ c ∈ A, a ≠ b ∧ a ≠ c ∧ b ≠ c ∧ a + b ∈ A ∧ a + c ∈ A ∧ b + c ∈ A
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:865

Reported activity

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

  • AI collaborating with humans

    Erdős AI contributions wiki · 21-22 Jun, 2026

    Machine
    GPT-5.5 Pro
    People
    Ricky Cipollini
    Open the source record

  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    Ricky Cipollini
    Reported outcome
    resolved
    Open the source record

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