Essentially, i need this for a third year mathematics project and originally i thought i just needed to have something like this:
The group with this presentation is explicitly realized by the set of integers , under the operation of addition, where $a = 1$. Hence there exists an isomorphism from the infinite cyclic group of order $n$ to the integers mod $n$.
But i was told that i actually needed to show that there exists a free group that is generated by $a$, where $a$ is an element of the infinite cyclic group. Thank you.