incongruent integers

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October 8th 2009, 04:23 PM
dori1123

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 $p$ .
October 8th 2009, 05:43 PM
Bruno J.

Quote:

Originally Posted by dori1123

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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