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Math Help - Prove that [1] and [p-1] are their own multiplicative inverses

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    Prove that [1] and [p-1] are their own multiplicative inverses

    Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rainyice View Post
    Let p be a prime integer. Prove that [1] and [p-1] are the only elements in Zp that are their own multiplicative inverses.
    Is this supposed to be done group theoretically or number theoretically?
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    Quote Originally Posted by Drexel28 View Post
    Is this supposed to be done group theoretically or number theoretically?
    i think it is group because this problem is in the congruence classes section. thanks
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