# incongruent integers

• Oct 8th 2009, 05:23 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 $p$.
• Oct 8th 2009, 06:43 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.