Zn* is a group
Dependencies:
$\mathbb{Z}_n^*$ is a group under multiplication mod $n$.
Proof

Closure: $$a, b \in \mathbb{Z}_n^* \Rightarrow \gcd(a, n) = \gcd(b, n) = 1 \Rightarrow \gcd(ab, n) = 1 \Rightarrow ab \in \mathbb{Z}_n^* $$

Associativity: Multiplication modulo $n$ is associative.

Identity: 1 is identity.

Inverse: $a \in \mathbb{Z}_n^* \Rightarrow \gcd(a, n) = 1 \Rightarrow$ inverse of $a$ modulo $n$ exists.
Therefore, $\mathbb{Z}_n^*$ is a group.
Dependency for:
 Euler's Theorem Used in proof
Info:
 Depth: 4
 Number of transitive dependencies: 6