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Math Help - Elementary # theory

  1. #1
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    Elementary # theory

    Hey, could anyone help me establish the following statements:

    If a has order 2k modulo the odd prime p, then a^k= -1(mod p)
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  2. #2
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    Quote Originally Posted by felixmcgrady View Post
    Hey, could anyone help me establish the following statements:

    If a has order 2k modulo the odd prime p, then a^k= -1(mod p)
    Saying "a has order 2k modulo p" means that a^(2k)= 1 (mod p). Since p is a prime, either a^k= 1 or a^k= -1. If a^k= 1, then a has order k modulo p, not 2k.
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