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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