Suppose that $\displaystyle x \in \mathbb{Z_p^\times}$ has order $\displaystyle p-1$. Prove that the integers $\displaystyle x^1, x^2, ..., x^{p-1}$ are incongruent mod $\displaystyle p$.

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- Oct 8th 2009, 04:23 PMdori1123incongruent integers
Suppose that $\displaystyle x \in \mathbb{Z_p^\times}$ has order $\displaystyle p-1$. Prove that the integers $\displaystyle x^1, x^2, ..., x^{p-1}$ are incongruent mod $\displaystyle p$.

- Oct 8th 2009, 05:43 PMBruno J.