关于有限域上一类方程解的个数

On the Number of Solutions of Certain Equations over Finite Fields

中文关键词:  有限域  方程的解  特征标  容斥原理.

英文关键词:Finite fields  solutions of equation  multiplicative character  inclusion-exclusion principle.

中文摘要:

      设$\F_q$是$q=p^f$个元素的有限域,$p$是奇素数,用$N(a_1x_1^2 \cdots a_nx_n^2=bx_1\cdotsx_s)$表示方程$a_1x_1^2 \cdots a_nx_n^2=bx_1\cdots x_s$在$\F_q^n$中解的个数,这里 $n>5$, $s5$, $3\leq s

英文摘要:

      Let $\F_q$ be a finite field with $q=p^f$ elements, where $p$ is an odd prime. Let $N(a_1x_1^2 \cdots a_nx_n^2=bx_1\cdots x_s)$ denote the number of solutions $(x_1,\ldots,x_n)$ of the equation $a_1x_1^2 \cdots a_nx_n^2=bx_1\cdots x_s$ in $\F_q^n$, where $n>5$, $s5$, $3\leq s