数学杂志2017，Vol.37Issue(1)：138-144,7.
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 FINITE FIELDS WITH n UNKNOWNS AND WITH DEGREE n WHICH VANISH ONLY AT ZERO
摘要
Abstract
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.关键词
有限域/方程只有零解/多元多项式分解/不可约多项式Key words
finite field/equation which vanish only at zero/multivariate polynomial factorization/irreducible polynomial分类
数理科学引用本文复制引用
陈玺,屈龙江,李超..有限域上n 元n 次方程只有零解的充要条件[J].数学杂志,2017,37(1):138-144,7.基金项目
国家自然科学基金资助(61272484) （61272484）
信息保障科学技术实验室开放基金资助(KJ-12-02) （KJ-12-02）
