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Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields 被引量:2
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作者 HU Shuangnian WANG Shihan +1 位作者 LI Yanyan NIU Yujun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2023年第5期369-372,共4页
Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of H... Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results. 展开更多
关键词 finite field rational point diagonal equations Jacobi sums
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ON THE PRIORI ESTIMATE OF MAXIMUM MODULUS OF SOLUTIONS TO A SYSTEM OF DIAGONALLY DEGENERATE ELLIPTIC EQUATIONS 被引量:1
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作者 WANG Xiangdong RONG Haiwu LIANG Xiting (Mathematics Department of Foshan University, Foshan 528000, China) 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2003年第4期446-452,共7页
In this paper we first give an a priori estimate of maximum modulus ofsolutions for a class of systems of diagonally degenerate elliptic equations in the case of p > 2.
关键词 system of diagonally degenerate elliptic equations generalized solution priori estimate
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The Number of Solutions of Certain Equations over Finite Fields
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作者 HU Shuangnian LIU Jianghan QIN Zhentao 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第1期49-52,共4页
Let s be a positive integer,p be an odd prime,q=p^(s),and let F_(q)be a finite field of q elements.Let N_(q)be the number of solutions of the following equations:(x_(1)^(m_(1))+x_(2)^(m_(2))+…+x_(n)^(m_(n)))^(k)=x_(1... Let s be a positive integer,p be an odd prime,q=p^(s),and let F_(q)be a finite field of q elements.Let N_(q)be the number of solutions of the following equations:(x_(1)^(m_(1))+x_(2)^(m_(2))+…+x_(n)^(m_(n)))^(k)=x_(1)x_(2)…x_(n)x^(k_(n+1))_(n+1)…x^(k_(t))_(t)over the finite field F_(q),with n≥2,t>n,k,and k_(j)(n+1≤j≤t),m_(i)(1≤i≤n)are positive integers.In this paper,we find formulas for N_(q)when there is a positive integer l such that dD|(p^(l)+1),where D=1 cm[d_(1),…,d_(n)],d=gcd(n∑i=1M/m_(i)-kM,(q-1)/D),M=1 cm[m_(1),…,m_(n)],d_(j)=gcd(m_(j),q-1),1≤j≤n.And we determine N_(q)explicitly under certain cases.This extends Markoff-Hurwitz-type equations over finite field. 展开更多
关键词 finite field rational point diagonal equation Markoff-Hurwitz-type equations
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