&&x = \sqrt{D}, \\ &&p_0 = 0, \\ &&q_0 = 1, \\ &&a_k =\lfloor \frac{x p_k}{q_k} \rfloor, \;\; k \ge 0, \\ &&p_{k 1} = a_k Q_k - p_k, \;\; k \ge 0, \\ &&q_{k 1} = \frac{D - p_{k 1}^2}{q_k}, \;\; k \ge 0.
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