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Math Help - Congruences and fields

  1. #1
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    Congruences and fields

    Let p be a prime number. Use the fact that Zp is a field to prove that (p-1)! is congruent to -1(mod p).

    Hint: Pair elements of Zp with their multiplicative inverses.
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  2. #2
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    Quote Originally Posted by meggnog View Post
    Let p be a prime number. Use the fact that Zp is a field to prove that (p-1)! is congruent to -1(mod p).

    Hint: Pair elements of Zp with their multiplicative inverses.

    That is a huge hint: what've you done so far?

    Tonio
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