【摘要】 设m和n是二个正整数,f（x₁,…,x_n）是一个整系数多项式,如果同余式f（x₁,…,x_n）≡a（modm）对所有的整数a均有m^n-1个解,则称f（x₁,…,x₂）是一个模m的置换多项式.一个基本的问题是:如何决定一个多项式是否置换多项式,如果m是素数,已知一些判别方法.在本文中,我们研究m为复合数的情形.更多还原

【Abstract】 Let m and n be two positive integers. A polynomial f(x1,. . .xi) with integral coefficients is called a permutation polynomial modulo m if the congruence f(x1,…xn) = a (mod m) has mn-1 solutions for all integers a . A basis question is to determine when a polynomial is a permutation polynomial modulo m .If mis a prime number, several criterion are known. In this paper,we study the case when m is a composite number.更多还原