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Necessary conditions for reversed Dickson polynomials to be permutational. (English) Zbl 1209.11103
Let $$\mathbb F_q$$ be a finite field with $$q$$ elements. Let $$n\geq 0$$ be an integer then the polynomial $$D_n(x,y)\in \mathbb Z[x,y]$$, defined by $$D_n(x+y,xy)=x^n+y^n$$ gives the reversed Dickson polynomial $$D_n(a,x)$$ when $$a$$ is a fixed element of the finite field $$\mathbb F_q$$. It is a well known problem to determine when the reversed Dickson polynomial is a permutation polynomial over a finite field. The authors of the paper under review give a several necessary conditions for which this polynomial is a permutation polynomial over $$\mathbb F_q$$.

##### MSC:
 11T06 Polynomials over finite fields 11C08 Polynomials in number theory
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##### References:
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