Skip to content

Erdős problem 867

Start work

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)?

Sources

The source's own material, retained exactly.

6 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

867.lean

Retained formal statement2 of 6

Adenwalla has observed that ∣A∣≤(23+o(1))N.\lvert A\rvert \leq (\tfrac{2}{3}+o(1))N.

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.adenwalla2 linesExact file
∀ (ε : ℝ),  0 < ε → ∀ᶠ (N : ℕ) in Filter.atTop, ∀ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A → ↑A.card ≤ (2 / 3 + ε) * ↑N
SolvedStatement only, no proof