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Math Help - incongruent integers

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    incongruent integers

    Suppose that x \in \mathbb{Z_p^\times} has order p-1. Prove that the integers x^1, x^2, ..., x^{p-1} are incongruent mod p.
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    Quote Originally Posted by dori1123 View Post
    Suppose that x \in \mathbb{Z_p^\times} has order p-1. Prove that the integers x^1, x^2, ..., x^{p-1} are incongruent mod p.
    This is precisely what it means for x to have order p-1.
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