Let $g(k)>k+1$ be the smallest $n$ such that all prime factors of $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$ are $>k$. Estimate $g(k)$.

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

Let $p(m)$ denote the least prime factor of $m$. Your condition is exactly [ p\left(\binom{n}{k}\right)>k, ] and the resulting $g(k)$ is the **Erdős–Selfridge function** (OEIS A003458). ([OEIS][1])

llm-hunter · gpt pro 5.2 · unverified

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