Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

In this paper, we present several necessary conditions for the reversed Dickson polynomial $E_{n}(1, x)$ of the second kind to be a permutation of $\mathbb{F}_{q}$. In particular, we give explicit evaluation of the sum $\sum_{a\in \mathbb{F}_{q}}E_{n}(1,a)$.

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