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## Factorials

2! = 2, 3! = 3*2, 4! = 4*3*2… and 100! is a lot better than writing out 158 digits. 90! is the largest factorial that can fit in a tweet.

# Wilson's Theorem

What is $$28 ! \pmod{29} ?$$

What is $$59 ! \pmod{61} ?$$

What is $$(18 !)^2 \pmod{19} ?$$

What is $$(10 !)^ {84} \pmod{11} ?$$

If $$(n-1)! \equiv -1 \pmod{n} ,$$ where $$n$$ is an integer larger than one, which of the following is true?

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