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In a recent paper, Akbary and Wang gave a sufficient condition for x^u + x^rto permute GF(q), in terms of the period of a certain sequence involving sumsof cosines. As an application they gave necessary and sufficient conditions incase u,r,q satisfy certain special properties. We show that the Akbary-Wangsufficient condition follows from a more general sufficient condition whichdoes not involve sums of cosines. This leads to vastly simpler proofs of theAkbary-Wang results, as well as generalizations to polynomials of the formx^r*h(x^{(q-1)/d}).

On some permutation polynomials over F_q of the form x^r*h(x^((q-1)/d)))