Generators of Additive Group of Integers

Theorem
The only generators of the additive group of integers $\struct {\Z, +}$ are $1$ and $-1$.

Proof
From Integers under Addition form Infinite Cyclic Group, $\struct {\Z, +}$ is an infinite cyclic group generated by $1$.

From Generators of Infinite Cyclic Group, there is only one other generator of such a group, and that is the inverse of that generator.

The result follows.