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Article On a Class of Permutation Trinomials Over Finite Fields(Tubitak Scientific & Technological Research Council Turkey, 2024) Temür, Burcu Gülmez; Özkaya, BuketIn this paper, we study the permutation properties of the class of trinomials of the form f (x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficient conditions on λ1 and λ2 such that f (x) permutes Fq2 , where q is odd and q = 22k+1, k ∈