Let $p$ be a prime and$$A_p=\{k!(\mathrm{mod}p):1\le k<p\}.$$Is it true that$$|A_p|\sim (1-\frac{1}{e})p?$$

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

Your statement is exactly a long‑standing conjecture (usually attributed to Stauduhar, and also appearing in Guy’s *Unsolved Problems in Number Theory*): if [ h(p):=|\\{1!,2!,\dots,(p-1)!\\}|\pmod p=\lvert A_p\rvert, ] then [ \frac{h(p)}{p}\ \longrightarrow\ 1-\frac1e\qquad (p\to\infty). ] This is stated explicitly as …

llm-hunter · gpt pro 5.2 · unverified

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