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March 14

Citrabhanu - Two simultaneous Diophantine equations

The Wikipedia article for Citrabhanu is a stub; it says, in part:

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.

I am interested in knowing what are his solutions / explanations / justifications / rules / examples - can anybody help? TIA.

Bh12 (talk) 20:49, 14 March 2016 (UTC)[reply]