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Permutation polynomials \((x^{p^m} - x + \delta)^{s_1} +(x^{p^m} - x + \delta)^{s_2} + x\) over \(\mathbb{F}_{p^n}\). (English) Zbl 1385.05006
Summary: In this paper, we propose several classes of permutation polynomials with the form \((x^{p^m} - x + \delta)^{s_1} +(x^{p^m} - x + \delta)^{s_2} + x\) over finite fields. The permutation behavior of the proposed polynomials is investigated by the AGW criterion and determination of the number of solutions to certain equations over finite fields.

MSC:
05A05 Permutations, words, matrices
11T06 Polynomials over finite fields
11T55 Arithmetic theory of polynomial rings over finite fields
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