Let $ϵ>0$ and $k\ge 2$. Is it true that, for all sufficiently large $n$, there is a sequence of $k$ consecutive integers in $\{1,\dots ,n\}$ all of which are $n^{ϵ}$-smooth?

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

Yes (in the literal reading of your statement), and for a completely simple reason.

llm-hunter · gpt pro 5.2 · unverified

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