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In this paper we determine b ∈ Fqn for which the polynomial f(x) = x + bx ∈ Fqn [x] is a permutation polynomial and determine b ∈ Fqn for which the polynomial f(x) = x + bx ∈ Fqn [x] is a complete permutation polynomial where s = q −1 t , t ∈ Z such that t | q − 1 .

Some permutations and complete permutation polynomials over finite fields