摘要
设p为奇素数,Fp是含p个元素的有限域,n是大于1的自然数.通过方程的秩r,对Fp上n元二次方程进行了分类,若r=1,Fp上n元二次方程除(p-1)/2个外,其余都有解;若r>1,Fp上n元二次方程都有解,给出了各类方程的解数.
Let p be an odd prime, Fp be the finite field with p elements, and natural number n 〉 1 . By rank r of equations, quadratic equations with n variables over Fp is assorted. If r = 1 , there are solutions for quadratic equations with n variables over Fp besides (p - 1)/2 equations. If r 〉 1 ,there are solutions for quadratic equations with n variables over Fp . The numbers of solutions of quadratic equations with n variables over Fp have been given for every class equation.
出处
《江西师范大学学报(自然科学版)》
CAS
北大核心
2005年第4期298-301,共4页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
云南省教育科研课题资助项目(2000308).
关键词
有限域
二次方程
方程的解数
方程的秩
二次剩余
finite field
quadratic equations
the numbers of solutions of equations
rank of equations
quadratic residue