中文摘要：

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.

英文摘要：

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 sufficient 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.