有限域上n元n次方程只有零解的充要条件
THE STRUCTURE OF THE EQUATION OVER FLNITE FLELDS WITH n UNKNOWNS AND WITH DEGREE n WHICH VANISH ONLY AT ZERO

本文研究了有限域上只有零解的n元n次方程的结构问题.利用对有限域上不可约多元多项式在其扩域中的分解特征的刻画，结合Chevalley定理，得到了有限域上n元n次方程只有零解的一个充要条件，并给出这类方程的一些新的具体构造.
In this paper, we investigate the structure of the equation over finite fields with n unknowns and with degree n which vanish only at zero. By using the factorization of the irreducible multivariable polynomial in some extension field and with the Chevalley Theorem, a su-cient and necessary condition of the equation with n unknowns and with degree n which vanish only at zero is obtained. Furthermore, we construct some explicit equations of this class