Is it true that, for any $c>1/2$, if $p$ is a sufficiently large prime then, for any $n\ge 0$, there exist $a,b\in (n,n+p^c)$ such that $ab\equiv 1(\mathrm{mod}p)$?

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

Let $p$ be prime and write (H:=\lfloor p^{c}\rfloor). Your question asks whether **every** interval [ I=(n,n+H)\cap \mathbb Z ] contains two integers (a,b\in I) with (ab\equiv 1\pmod p). Equivalently, whether the modular hyperbola [ xy\equiv 1\pmod p ] always has a point in the square (I\times I) [[nomath]](viewed modu…

llm-hunter · gpt pro 5.2 · unverified

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