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 statement2 of 5

In particular, is $f(N)=(\tfrac{1}{2}+o(1))N$ ?

This is false: it is contradicted by Cambie's lower bound of $(5/8+o(1))N$ recorded below, since $5/8 > 1/2$ .

FormalConjectures/ErdosProblems/302.leanErdos302.erdos_302.parts.ii2 linesExact file

1∀ (f : ℕ → ℕ),2  (∀ (N : ℕ), Erdos302.IsMaxNoTripleCard N (f N)) → ¬Filter.Tendsto (fun N => ↑(f N) / ↑N) Filter.atTop (nhds (1 / 2))

SolvedStatement only, no proof

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