Some permutations and complete permutation polynomials over finite fields

Abstract

In this paper we determine $bin F_{q^n}^ast$ for which the polynomial $f(x)=x^{s+1}+bxin F_{q^n}left[xright]$ is a permutationpolynomial and determine $bin F_{q^n}^ast$ for which the polynominal $f(x)=x^{s+1}+bxin F_{q^n}left[xright]$ is a complete permutationpolynomial where $s=frac{q^n-1}t,;tinmathbb{Z}^+$ such that $left.t;right|;q^n-1$.