有限域上一类方程在（F^＊）^n中的解数公式

The Number of Solutions of a Cubic Equation in over a Finite Field

设F=Fq是一个q元有限域,F*=Fq*为其乘法群,q=pf,f≥1,p是一个奇素数。该文利用组合的方法给出了有限域上F=Fq上一类三次方程x1x2+x1x2x3+x2x3x4+…+xn-4xn-3xn-2+xn-1xn=b在(F*)n上解数的一个直接公式,这里b∈F=F。

Let F be a finite field with q = p^f elements and let F^＊ be the multiplicative group of nonzero elements of F, where q=p^f f≥ 1 is an odd prime number. In this paper, the author gives an explicit formula for the number of solutions of the following cubic equation by using some combinatorial methods：x1x2＋x1x2x3＋x2x3x4＋…xn-4xn-2＋xn-1xn=b in （F^＊）^n,where b∈F