# 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 $p$.
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.