Discussion
What is the remainder when \((21!)\) is divided by 23?
Answer: A
This problem is an application of a corollary of Wilson's Theorem. Wilson's Theorem states that for any prime number p, \((p-1)! \equiv -1 \pmod{p}\).
A direct corollary of this theorem is that for a prime p, \((p-2)! \equiv 1 \pmod{p}\).
Here, p=23 (which is a prime number). We need to find the remainder of \( (23-2)! \) when divided by 23.
According to the corollary, \(21! \equiv 1 \pmod{23}\). The remainder is 1.
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