1. ## Prove H=mZ

Let $H$ be a subgroup of $(\mathbb{Z},+)$ with more than one element, and let $m$ be the smallest positive integer in $H \cap \mathbb{N}$. Prove that $H=m\mathbb{Z}$. [Hint: Use the Division Algorithm]

Question: Does $m\mathbb{Z}$ look like this:

$m\mathbb{Z}=\{0, \pm m, \pm 2m, \pm3m, \cdot \cdot \cdot\}$?

2. Originally Posted by novice
Let $H$ be a subgroup of $(\mathbb{Z},+)$ with more than one element, and let $m$ be the smallest positive integer in $H \cap \mathbb{N}$. Prove that $H=m\mathbb{Z}$. [Hint: Use the Division Algorithm]

Question: Does $m\mathbb{Z}$ look like this:

$m\mathbb{Z}=\{0, \pm m, \pm 2m, \pm3m, \cdot \cdot \cdot\}$?

Yes.

Tonio