A recursive method to calculate the number of solutions of quadratic equations over finite fields

Iyanaga, Kenichi

doi:10.1090/S0025-5718-1995-1297472-6

A recursive method to calculate the number of solutions of quadratic equations over finite fields
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Math. Comp. 64 (1995), 1319-1331 Request permission

Abstract:

The number ${S_m}(\alpha )$ of solutions of the quadratic equation \[ x_1^2 + x_2^2 + \cdots + x_m^2 = \alpha \quad (x_i^2 \ne \pm x_j^2\quad {\text {for}}\;i \ne j)\] 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.

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On the number of solutions of

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