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Math Help - Wilson's Theorem

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    Wilson's Theorem

    Use Wilson;s Theorem to find the least nonnegative residue modulo m of integer n

    n=30! m=31
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    Hello,
    Quote Originally Posted by bigb View Post
    Use Wilson;s Theorem to find the least nonnegative residue modulo m of integer n

    n=30! m=31
    Wilson's theorem : (p-1)! \equiv -1 (\bmod p) (where p is a prime integer)
    Here, p=31 and is prime.

    So 30! \equiv -1 (\bmod 31)

    But -1 \equiv 30 (\bmod 31)

    So answer is 30, since you want the least nonnegative residue.
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