In the link given, it is proven that $\operatorname{Aut}( \Bbb Z_n)$ is isomorphic with $U_n$.
I understood the proof until the last line where it says
since, $T(\alpha) = \alpha(1) = r$, $T$ is onto.
Why is $T$ onto when $T(\alpha) = r$?
2026-04-01 05:48:14.1775022494
Why is the function $T=\alpha(1)$ from ${\rm Aut}(\Bbb Z_n)$ to $U_n$ surjective?
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