Erdős problem 867 · problems.science

Is it true that if $A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\}$ has no solutions to $a_i+a_{i+1}+\cdots+a_j\in A$ then $\lvert A\rvert \leq \frac{N}{2}+O(1)?$

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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

867.lean

Retained formal statement6 of 6

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

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.lower_bound1 lineExact file

1∃ C, ∀ (N : ℕ), ∃ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A ∧ ↑N / 2 - C ≤ ↑A.card

SolvedStatement only, no proof

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