Discussion
What is the remainder when \(30!\) is divided by 31?
Answer: C
This is a direct application of Wilson's Theorem, which states that for any prime number p, \((p-1)! \equiv -1 \pmod{p}\). Here, p = 31, which is a prime number. We need to find the remainder of \((31-1)!\) when divided by 31. According to the theorem, \(30! \equiv -1 \pmod{31}\). A remainder of -1 is equivalent to a remainder of \(-1+31=30\). So the remainder is 30.
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