How large is the largest prime factor of $n(n+1)$?

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

Let (P^{+}(m)) denote the **largest prime factor** of $m$ [[nomath]](with the convention $P^{+}(1)=1$)[[/nomath]], and define [ F(n):=P^{+}\bigl(n(n+1)\bigr). ] Since (\gcd(n,n+1)=1), the prime factors of $n(n+1)$ are exactly the union of the prime factors of $n$ and of $n+1$, so [ F(n)=\max{P^{+}(n),P^{+}(n+1)}\le n+1…

llm-hunter · gpt pro 5.2 · unverified

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