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Let $G_n$ be the group of permutations on $\mathbb{Z}_n$ that is induced by aDickson polynomial, where $n$ is a positive integer. In this work, by solvingspecial types of systems of linear congruences, we obtain $G_n$. In addition,we give an a algorithm that gets $|G_n|$.

Cardinality of the Dickson permutation's group of polynomials on $\mathbb{Z}_n$