【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),m
【机 构】
：
School of Mathematics and Statistics,Nanyang Institute of Technology,Nanyang 473004,Henan,China;Coll
论文部分内容阅读
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.
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