formula

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