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Erdős problem 867

Is it true that if A={a1<⋯<at}⊆{1,…,N}A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\} has no solutions to ai+ai+1+⋯+aj∈Aa_i+a_{i+1}+\cdots+a_j\in A then ∣A∣≤N2+O(1)?\lvert A\rvert \leq \frac{N}{2}+O(1)?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/867.lean

Formal Conjectures

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_8671 lineExact file
False ↔ ∃ C, ∀ (N : ℕ), ∀ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A → ↑A.card ≤ ↑N / 2 + C
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:867
  • PLBY Lean proofsErdosProblems.Erdos867

Reported activity

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

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