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Erdős problem 867

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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)?

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6 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

867.lean

Retained formal statement6 of 6

Taking A=(N/2,N]∩NA=(N/2,N]\cap \mathbb{N} shows ∣A∣≥N/2−O(1)\lvert A\rvert \geq N/2-O(1) is possible.

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.lower_bound1 lineExact file
∃ C, ∀ (N : ℕ), ∃ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A ∧ ↑N / 2 - C ≤ ↑A.card
SolvedStatement only, no proof