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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.[1] These types are all the possible pairs of equations of the following seven forms:[2]

\ 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.


  1. ^ Joseph, George Gheverghese (2009), A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, SAGE Publications India, p. 21, ISBN 9788132104810 .
  2. ^ Hayashi, Takao; Kusuba, Takanori (1998), "Twenty-one algebraic normal forms of Citrabhānu", Historia Mathematica 25 (1): 1–21, doi:10.1006/hmat.1997.2171, MR 1613702 .