Indeterminate Equations of the First Degree

Āryabhaṭa I (476) was the earliest Hindu Algebraist worked on the Indeterminate Equations of the First Degree. He provided a method for solving the simple indeterminate equation

$by-ax=c$

where a, b and c are integers.He also provided how to extend this to solve Simultaneous Indeterminate Equations of the first degree.

Bhāskara I (522) disciple of Āryabhaṭa I has displayed that the same method might be applied to solve the equation

$by-ax=-c$

and further that the solution of this equation would follow from that of

$by-ax=-1$

Brahmagupta and others followed the methods of Āryabhaṭa I and Bhāskara I

Importance

The subject of indeterminate analysis of the first degree was considered so important by ancient Hindu Algebraists that the whole science of algebra was once named after it. Āryabhaṭa II , Bhāskara II and others mentions precisely along with the sciences of arithmetic, algebra and astronomy.

On account of its special importance exclusive work on this entitled kuṭṭākāra śiromaṇi by Devarāja a commentator of of Āryabhaṭa I.