Erdős Problem #535

The problem

Let $r\geq 3$ , and let $f_r(N)$ denote the size of the largest subset of $\{1,\ldots,N\}$ such that no subset of size $r$ has the same pairwise greatest common divisor between all elements. Estimate $f_r(N)$ .

Statement quoted from erdosproblems.com/535, maintained by Thomas Bloom. Original source: [Er69][Er70][Er73]. 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.

Date	Kind	AI systems	Humans	Outcome
27 Apr, 2026	AI working with humans	GPT-5.5 Thinking	Kireet Cheri, Sourish Kumrawat, Hrishi Sunder	🟡 Partial result (implicit in literature)

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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