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Number Theory

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Using Wilson's Theorem

NUMTH-T31BD5

Wilson's theorem will be very helpful with this problem.

Wilson's Theorem: Let $p > 1$ be a prime number. Then, $(p - 1)! \equiv -1(\text{mod}~p)$.

Which of the following statements are true? Select ALL that apply.

A

$6! \equiv 0(\text{mod}~7)$

B

$18! \equiv -1(\text{mod}~19)$

C

$16! \equiv -1(\text{mod}~17)$

D

$16! \equiv 1(\text{mod}~17)$