The Subgroup $n\mathbb{Z}$

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Definition (The Subgroup $n\mathbb{Z}$)

For each $n\in \mathbb{N}$ we define $n\mathbb{Z}$ to be the subgroup $\langle n\rangle = \{kn\mid k\in \mathbb{Z}\}$ of the group $\mathbb{Z}$ under addition. This is just the multiples of $n$.

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