8. Find the remainder when $30!-1$ is divided by 930 .
Answer: 29
Solution: Since 31 is prime, by Wilson's Theorem, we obtain $30!-30 \equiv 0(\bmod 31)$. Because $30!-30 \equiv$ $\overline{0(\bmod 30)}$ and $\operatorname{gcd}(30,31)=1$, we get $30!-30 \equiv 0(\bmod 930)$. Therefore, $30!-1 \equiv 29(\bmod 930)$.