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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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FormalConjectures/ErdosProblems/

867.lean

Retained formal statement3 of 6

The current best bounds are due to Coppersmith and Phillips [CoPh96], who prove that the maximal size of such an AA satisfies 1324N−O(1)≤∣A∣.\frac{13}{24}N -O(1)\leq \lvert A\rvert.

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.coppersmith_phillips_lower_bound1 lineExact file
∃ C, ∀ (N : ℕ), ∃ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A ∧ 13 / 24 * ↑N - C ≤ ↑A.card
SolvedStatement only, no proof