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Math Help - Existence of Primitive Roots

  1. #1
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    Existence of Primitive Roots

    By definition, the positive integers that have a primitive root are 2, 4 and integers of the form p^t and 2p^t where p is a prime and t is a positive integer.

    Then why does 16 NOT have a primitive root? 16 = 2^4 and 2 is prime and 4 is a positive integer.

    I'm confused...
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  2. #2
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    Re: Existence of Primitive Roots

    You are missing one key word in your definition. There exists a primitive root (mod n) if and only if n = 1, 2, 4, p^\alpha, 2p^\alpha, where p is an odd prime.
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