Let $g(n)$ be minimal such that for any $A\subseteq [2,\infty )\cap \mathbb{N}$ with $|A|=n$ and any set $I$ of $\max (A)$ consecutive integers there exists some $B\subseteq I$ with $|B|=g(n)$ such that$$\prod _{a\in A}a\mid \prod _{b\in B}b.$$Is it true that$$g(n)\le (2+o(1))n?$$Or perhaps even $g(n)\le 2n$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Interpreting your definition in the standard way (and the only way that makes a nontrivial asymptotic question possible), one takes

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.