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 $\lvert A\rvert \leq \frac{N}{2}+O(1)?$

Sources

Browse retained paths and inspect the exact material available for this Problem.

6 retained statements2415f78e850a

Open selected source

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 $A$ satisfies $\frac{13}{24}N -O(1)\leq \lvert A\rvert.$

FormalConjectures/ErdosProblems/867.leanErdos867.erdos_867.variants.coppersmith_phillips_lower_bound1 lineExact file

1∃ C, ∀ (N : ℕ), ∃ A ⊆ Finset.Icc 1 N, Erdos867.ConsecutiveSumFree A ∧ 13 / 24 * ↑N - C ≤ ↑A.card

SolvedStatement only, no proof

Sources

Search problems.science