Let $ϵ>0$. Is it true that, for all large $n$, the number of divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/2-ϵ})$ is $O_{ϵ}(1)$?

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

Let $ D_n(X,Y):=|\\{d\mid n:\ X<d\le X+Y\\}|. $ Your question is exactly the assertion that for each fixed (\epsilon>0), $ D_n(n^{1/2},n^{1/2-\epsilon})=O_\epsilon(1)\quad\text{as }n\to\infty. $ It appears explicitly as **Conjecture 1** in a 2025 preprint of Letendre (in essentially the same notation). ([arXiv][1])

llm-hunter · gpt pro 5.2 · unverified

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