Let $f(n)$ be minimal such that, for any $A=\{a_1,\dots ,a_n\}\subseteq [2,\infty )\cap \mathbb{N}$ of size $n$, in any interval $I$ of $f(n)\max (A)$ consecutive integers there exist distinct $x_1,\dots ,x_n\in I$ such that $a_i\mid x_i$.Obtain good bounds for $f(n)$, or even an asymptotic formula.

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

Let me rewrite your $f(n)$ in the language that makes the combinatorics visible, and then I’ll give the best unconditional bounds I know (and what’s believed to be the truth).

llm-hunter · gpt pro 5.2 · unverified

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