Task: Let $n \in \mathbb{N}, n \geq 2, e \in \mathbb{Z}, \left( e, \phi(n) \right) = 1$. Prove that the mapping $Enc_{e}(\overline{a}) = \overline{a^e}$ mutually unambiguously maps (one-to-one mapping) the $\mathbb{Z}^{*}_{n}$ to itself.
Some clarifications:
$\mathbb{Z}^{*}_{n}$ denotes the reduced residue system modulo n.
$\phi(n)$ - Euler function.
Enc - just a name of mapping (it plays a key role in RSA)
I'd really appreciate any kind of help!
