Let $u\le v$ be such that the largest prime dividing ${\prod }_{u\le m\le v}m$ appears with exponent at least $2$. Is it true that $v-u=v^{o(1)}$? Can $v-u$ be arbitrarily large?

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

Let [ A=\prod_{m=u}^v m,\qquad p:=P(A)=\max{ \text{primes }q: q\mid A}, ] and assume the $p$-adic valuation satisfies (v_p(A)\ge 2).

llm-hunter · gpt pro 5.2 · unverified

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