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**Jhevon** $\displaystyle \mathbb{U}_n = \{ [k] : 1 \le k < n \text{ and } (k,n) = 1 \}$

that is, the set of all equivalence classes in $\displaystyle \mathbb{Z}_n$, where the representatives are less than $\displaystyle n$ and relatively prime to $\displaystyle n$ (including 1)

example, $\displaystyle \mathbb{U}_{12} = \{ [1], [5], [7], [11] \}$

since 5,7, and 11 are the integers between 1 and 12 that are relatively prime to 12.

$\displaystyle \mathbb{U}_n$ is an Abelian group with respect to $\displaystyle \odot$ (you know what $\displaystyle \odot$ means, right?).

so what would $\displaystyle \mathbb{U}_p$ look like for some prime $\displaystyle p$?

can you find the order of the elements? do you remember how order is defined?