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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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