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Let p be a prime and q a power of p. We study the permutation properties of the polynomial g n,q ∈ F p [x] defined by the functional equation a∈Fq (x + a) n = g n,q (x q − x). The polynomial g n,q is a q-ary version of the reversed Dickson polynomial in characteristic 2. We are interested in the parameters (n, e; q) for which g n,q is a permutation(More)