The group $(\Bbb Z_{13}\setminus \{0\}, \cdot)$ is cyclic. Determine all its generators.

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The group $(\Bbb Z_{13}\setminus \{0\}, \cdot)$ is cyclic. Determine all its generators.

How should I perform to check this by some permutations?

Like $cycle(1) = 2, cycle(2) = 3$ from the set of natural numbers?