Subgroup of integers I know that the only possible subgroups of $\mathbb Z$ are of the form $m\mathbb Z$. But how can I prove that these are the only possible subgroups?

Prove the following two intermediate results:


*

*If a subgroup of $\Bbb Z$ contains some number $m$, then it contains $m\Bbb Z$

*If a subgroup of $\Bbb Z$ contains two numbers $m,n$, then it contains $\gcd(m,n)$


Now let $k$ be the smallest positive integer in your subgroup. If there is an element $a\notin k\Bbb Z$ in the subgroup, reach a contradiction.
