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 $a+b,a+c,b+c\in A$ .

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

865.lean

Retained formal statement4 of 4

Choi, Erdős, and Szemerédi [CES75] have proved that, for all $k\geq 3$ , there exists $\epsilon_k>0$ such that (for large enough $N$ ) $f_k(N)\leq \left(\frac{2}{3}-\epsilon_k\right)N$ .

FormalConjectures/ErdosProblems/865.leanErdos865.erdos_865.variants.upper_bound1 lineExact file

1∀ (k : ℕ), 3 ≤ k → ∃ ε > 0, ∀ᶠ (N : ℕ) in Filter.atTop, ↑(Erdos865.f N k) ≤ (2 / 3 - ε) * ↑N

SolvedStatement only, no proof

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