Erdős problem 302 · problems.science

Let $f(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there are no solutions to $\frac{1}{a}= \frac{1}{b}+\frac{1}{c}$ with distinct $a,b,c\in A$ ? Estimate $f(N)$ .

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

302.lean

Retained formal statement3 of 5

Stijn Cambie has observed that $f(N)\geq (5/8+o(1))N,$ taking $A$ to be all odd integers $\leq N/4$ and all integers in $[N/2,N]$ .

FormalConjectures/ErdosProblems/302.leanErdos302.erdos_302.variants.lower_five_eighths3 linesExact file

1∀ (f : ℕ → ℕ),2  (∀ (N : ℕ), Erdos302.IsMaxNoTripleCard N (f N)) →3    ∀ (ε : ℝ), 0 < ε → ∀ᶠ (N : ℕ) in Filter.atTop, (5 / 8 - ε) * ↑N ≤ ↑(f N)

SolvedStatement only, no proof

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