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Mathematics of Computation

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


Author: Kenichi Iyanaga
Journal: Math. Comp. 64 (1995), 1319-1331
MSC: Primary 11T30; Secondary 11D79, 11R29, 11Y16
DOI: https://doi.org/10.1090/S0025-5718-1995-1297472-6
MathSciNet review: 1297472
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Abstract: The number $ {S_m}(\alpha )$ of solutions of the quadratic equation

$\displaystyle x_1^2 + x_2^2 + \cdots + x_m^2 = \alpha \quad (x_i^2 \ne \pm x_j^2\quad {\text{for}}\;i \ne j)$

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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1995-1297472-6
Keywords: Quadratic equations over a finite field, number of solutions, algorithm
Article copyright: © Copyright 1995 American Mathematical Society