Citrabhanu

Citrabhānu (fl. 1530) was a mathematician from the Kerala school in the 16th century. He gave integer solutions to 21 types of systems of two simultaneous Diophantine equations in two unknowns. These types are all the possible pairs of equations of the following seven forms:

$\ x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g$

For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric.