Mathematics in Ancient and Medieval India c7.s5.153

c7.s5.153

The term *vargaprakṛti* has been used by Indian scholars to designate the equations of the type Nx² ± c = y². The most fundamental equation of this type has been regarded as Nx² ± 1 = y². Brahmagupta ( 628 A. D. ) first gave solutions in rational integers of both of these types. Further refinements, clarifications, extensions were made by subsequent mathematicians such as Śrīpati, Bhāskara II, *Nārāyaṇa* and others including several commentators who rendered considerable service to this branch of algebra. Here N is termed as *guṇakaprakṛti*, x : kaniṣṭhapada, hrasvamūla, or *ādyamūla*, y : jyeṣṭhapada, or *anyamūla*; c : kṣepa, *prakṣepa* or *prakṣepaka*.