有限域上多项式的根与质数模高次同余方程

The Roots of Polynomials over a Finite Field and Prime Number Model Higher Degree Congruence Equations

得到了有限域上多项式根的一些结果及一个判断质数模高次同余方程有解及解的个数的方法，并且对任意一个以ｐ为模的高次同余方程，都可以通过解一个次数不超过ｐ－１２的同余方程来确定其解，次数不超过ｐ－１２的同余方程的解的个数等于其次数；还得到了判别一个数的平方剩余的方法。

Some results about the roots of polynomials over a finite field and the method to judge the solution and solution number of prime number model congruence equation are given.For any higher degree gongruence equation with p as model ,its solution can be determined by solving a congruence equation in no less than (p-1)/2 number ,It's number is equal to its degree. Besides,a method to judge the square residue of a number is obtained.