Erdős problem 126 · problems.science

Let $f(n)$ be maximal such that if $A\subseteq\mathbb{N}$ has $|A| = n$ then $\prod_{a\neq b\in A}(a + b)$ has at least $f(n)$ distinct prime factors. Is it true that $\frac{f(n)}{\log n} \to\infty$ ?

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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

126.lean

Retained formal statement3 of 3

Erdős says that $f(n) = o(\frac{n}{\log n})$ has never been proved.

FormalConjectures/ErdosProblems/126.leanErdos126.erdos_126.variants.isLittleO1 lineExact file

1∀ (f : ℕ → ℕ), Erdos126.IsMaximalAddFactorsCard f → (fun n => ↑(f n)) =o[Filter.atTop] fun n => ↑n / Real.log ↑n

OpenStatement only, no proof

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