Erdős Problem #536

The problem

Let $f(N)$ be the largest size of $A\subseteq \{1,\ldots,N\}$ with the property that there are no distinct $a,b,c\in A$ such that

$$[a,b]=[b,c]=[a,c],$$

where $[a,b]$ denotes the least common multiple.

Estimate $f(N)$ - in particular, is it true that $f(N)=o(N)$?

Statement quoted from erdosproblems.com/536, maintained by Thomas Bloom. Original source: [Er64,p.646][Er70,p.124][Er73,p.124]. 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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