The expertise in Kuaka and Vargaprakti, the methods used for the solution of first and second degree indeterminate equations respectively, were considered pre-requisite qualifications of an Acharya in ancient and medieval India.. For solution of Kuka of the type; b y = a x + c, the values of were approximated from the successive divisions of a by b as in HCF process and the number of steps was reduced with choice of a desired quantity [mati] at any step, even or odd . The solution of Vargaprakti of the type, N x 2± c = y 2 [where N = a non-square integer, and c = kepa quantity] was in the manipulation of the value of √N→ based on two set of arbitrary values for x , y, and c and their cross multiplication when c = ± 1, ± 2, ± 4, as given by Brahmagupta (c. 628 CE). The solution was concretized by Jayadeva [1100 CE] and Bhāskara II [1150 CE] by a process, known as Cakravāla. The number of steps used in Cakravāla is much lower than the regular and half-regular expansions for √N used by Euler and Lagrange. The minimization property of Cakravāla is unique and the method may be treated as one of the major achievements of Indian mathematics in the history of solution of second degree equations.

中文翻译：

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Kuttaka和Vargaprakrti解决方案的某些功能

Kuaka和Vargaprakti的专业知识（分别用于求解一阶和二阶不定方程的方法）被认为是古代和中世纪印度Acharya的先决条件。该类型的; 如在HCF方法中，通过a ＝ b + c，由a除以b的连续除法来近似a的值，并且通过在任何步骤（偶数或奇数）上选择期望的量mati来减少步骤的数量。类型Vargaprakti的解为N x 2±c = y 2 [其中N =一个非平方整数，并且c = k•epa数量]是基于两个的√N→值的操作由Brahmagupta（c.628 CE）给出的x，y和c的任意值的集合，以及当c =±1，±2，±4时的交叉乘积。Jayadeva [1100 CE]和BhāskaraII [1150 CE]通过称为Cakravāla的方法将溶液具体化。在Cakravāla中使用的步数远低于Euler和Lagrange使用的√N的正则和半正则扩展。Cakravāla的极小化性质是独特的，该方法可被视为印度数学在二阶方程解历史上的主要成就之一。