Permutation Polynomials modulo $p^n$}

Abstract

A polynomial $f$ over a finite ring $R$ is called a \textit{permutation polynomial} if the mapping $R\rightarrow R$ defined by $f$ is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also present a new class of permutation binomials over finite field of prime order