A Recursive Method to Calculate the Number of Solutions of Quadratic Equations Over Finite Fields
Kenichi Iyanaga · Mathematics of Computation · 1995
The number ${S_m}(\alpha )$ of solutions of the quadratic equation \[ x_1^2 + x_2^2 + \cdots + x_m^2 = \alpha \quad (x_i^2 e \pm x_j^2\quad {\text {for}}\;i e j)\] for given m, with $\alpha$ and ${x_i}$ belonging to a finite field, is studied and a recursive method to compute ${S_m}(\alpha )$ is established.