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Math Help - Distinct residue modulo

  1. #1
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    Distinct residue modulo

    Hi

    Can someone kindly explain to me why in the sequence, they are all distinct?
    a mod p, a^2 mod p, a^3 mod ... are all distinct?

    If so, how do we know which element in the afrmentioned sequence is equal to the element in the sequence below:
    1 mod p, 2 mod p, ..., (p-1) mod p.

    Thanks.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Well they are not all distinct. Obviously there are at most p-1 possible values.

    It may happen that a, ..., a^{p-1} are all distinct. In this case we say a is a primitive root mod p. Generally though a is not a primitive root.
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