典型文献
The Number of Solutions of Certain Equations over Finite Fields
文献摘要：
Let sbea positive integer,p be an odd prime,q=ps,and let Fq be a finite field of q elements.Let Nq be the number of solutions of the following equations:(xm11+xm22+…+xmnn)k=x1x2…xnx(kn+1)(n+1)…xk1t over the finite field Fq,with n≥2,t＞n,k,and kj(n+1≤j≤t),mi(l≤i≤n)are positive integers.In this paper,we find formulas for Nq when there is a positive integer l such that dD|(pl+1),where D=lcm[d1,…,dn],d=gcd(n∑(n=1)M/mi-kM,(q-1)/D),M=lcm[m1,…,mn],dj=gcd(mj,q-1),1≤j≤n.And we determine Nq explicitly under certain cases.This extends Markoff-Hurwitz-type equations over finite field.
文献关键词：
中图分类号：
作者姓名：
HU Shuangnian;LIU Jianghan;QIN Zhentao
作者机构：
School of Mathematics and Statistics,Nanyang Institute of Technology,Nanyang 473004,Henan,China;College of Computer and Information Science,Southwest University,Chongqing 400715,China;School of Mathmatics and Computer,Panzhihua University,Panzhihua 617000,Sichuan,China
文献出处：
引用格式：
[1]HU Shuangnian;LIU Jianghan;QIN Zhentao-.The Number of Solutions of Certain Equations over Finite Fields)[J].武汉大学自然科学学报（英文版）,2022(01):49-52
A类：
sbea,xm11+xm22+,+xmnn,xnx,kn+1,xk1t,dD,pl+1,kM,Markoff
B类：
Number,Solutions,Certain,Equations,over,Finite,Fields,Let,positive,odd,prime,ps,let,Fq,finite,field,elements,Nq,number,solutions,following,equations,x1x2,kj,are,integers,In,this,paper,we,find,formulas,when,there,such,that,where,lcm,d1,dn,gcd,dj,mj,And,determine,explicitly,under,certain,cases,This,extends,Hurwitz,type
AB值：
0.508862
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机标中图分类号，由域田数据科技根据网络公开资料自动分析生成，仅供学习研究参考。
