Z/p^lZ上一类典型的多元奇异置换多项式

A Class of Typical Singular Permutation Polynomials in Several Indeterminates over Z/p^lZ

本文得到了一类典型模p奇异的n元多项式是模pl置换多项式的一个充分必要条件.特别地,对任意正整数u>1,本文得到了一个模pu的但不是pu+1的置换多项式.这些结果是对张起帆、胡永忠等人的若干已知结果的推广和改进.

In this note, the authors study a class of typical singular polynomials in several indeterminates modulo p and obtain a necessary and sufficient condition for them to be permutation polynomials modulo pl (l > 1). In particular, for any positive integer u > 1, the authors obtain a polynomial which is a permutation polynomial modulo pu but not modulo pu+1. These results are generalizations and improvement of some known results obtained by Zhang Qifan, Hu Yongzhong, et al.