# zbMATH — the first resource for mathematics

On some permutation polynomials over finite fields. (English) Zbl 1092.11046
Let $$q$$ be a prime power of the form $$q=7s+1$$. The authors classify the permutation binomials $$P(X)=X^r(1+X^{es})$$, $$1\leq e\leq 6$$, in terms of the sequence $$(a_n)$$ defined by $$a_n=a_{n-1}+2a_{n-2}-a_{n-3}$$, $$n\geq 3$$, with initial values $$a_0=3$$, $$a_1=1$$, and $$a_2=5$$. For prime powers of the form $$q=3s+1$$ and $$q=5s+1$$ the permutation behaviour of binomials was studied by L. Wang [Finite Fields Appl. 8, No. 3, 311–322 (2002; Zbl 1044.11103)]. For results on arbitrary permutation binomials see the authors’ paper [Proc. Am. Math. Soc. 134, No. 1, 15–22 (2006; Zbl 1137.11355)].

##### MSC:
 11T06 Polynomials over finite fields
##### Keywords:
permutation polynomials; finite fields; binomials
Full Text: