Erdős problem 865 · problems.science

There exists a constant $C>0$ such that, for all large $N$ , if $A\subseteq \{1,\ldots,N\}$ has size at least $\frac{5}{8}N+C$ then there are distinct $a,b,c\in A$ such that $a+b,a+c,b+c\in A$ .

Sources

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

4 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

865.lean

Retained formal statement2 of 4

It is a classical folklore fact that if $A\subseteq \{1,\ldots,2N\}$ has size $\geq N+2$ then there are distinct $a,b\in A$ such that $a+b\in A$ , which establishes the $k=2$ case.

FormalConjectures/ErdosProblems/865.leanErdos865.erdos_865.variants.k21 lineExact file

1∀ (N : ℕ), ∀ A ⊆ Finset.Icc 1 (2 * N), A.card ≥ N + 2 → ∃ a ∈ A, ∃ b ∈ A, a ≠ b ∧ a + b ∈ A

SolvedStatement only, no proof

Sources

Search problems.science