Erdős Problem #539

The problem

Let $h(n)$ be such that, for any set $A\subseteq \mathbb{N}$ of size $n$, the set

$$\left\{ \frac{a}{(a,b)}: a,b\in A\right\}$$

has size at least $h(n)$. Estimate $h(n)$.

Statement quoted from erdosproblems.com/539, maintained by Thomas Bloom. Original source: [Er73,p.125]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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