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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 \(\mathbb F_q\).

11T06 Polynomials over finite fields
11C08 Polynomials in number theory
Full Text: DOI
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