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The number S m (α) of solutions of the quadratic equation x 1 2 + x 2 2 +... + x m 2 = α (x i 2 # ±x j 2 for i # j) for given m, with α and x i belonging to a finite field, is studied and a recursive method to compute S m (α) is established.

A Recursive Method to Calculate the Number of Solutions of Quadratic Equations Over Finite Fields