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 $f(N)$ .

Sources

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

5 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

302.lean

Retained formal statement5 of 5

Wouter van Doorn has proved [va25] that $f(N) \leq (9/10+o(1))N.$

FormalConjectures/ErdosProblems/302.leanErdos302.erdos_302.variants.upper_nine_tenths3 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, ↑(f N) ≤ (9 / 10 + ε) * ↑N

SolvedStatement only, no proof

Sources

Search problems.science