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Some permuting trinomials over finite fields. (English) Zbl 0921.11062
Let \(\mathbb{F}_q\) be a finite field of \(q\) elements. Let \(d\) and \(r\) be positive integers satisfying \(d\mid (q-1)\). D. Wan and R. Lidl [Monatsh. Math. 112, 149-163 (1991; Zbl 0737.11040)] established necessary and sufficient conditions for a polynomial of the form \(x^r f(x^{(q-1)/d})\) to be a permutation polynomial of \(\mathbb{F}_q\). The present authors show that these conditions can be somewhat simplified in the case where \(d=3\) and the degree of \(f\) equals two.

MSC:
11T06 Polynomials over finite fields
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