# Chitrabhanu (mathematician)

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Chitrabhanu (IAST: Citrabhānu; fl. 16th century) was a mathematician of the Kerala school and a student of Nilakantha Somayaji. He is noted for a karaṇa, a concise astronomical manual, dated to 1530, an algebraic treatise, and a commentary on a poetic text. Nilakantha and he were both teachers of Shankara Variyar.[1][2]

## Contributions

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:[3]

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

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

## References

1. ^ a b Joseph, George Gheverghese (2009), A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, SAGE Publications India, p. 21, ISBN 9788132104810.
2. ^ Plofker, Kim (2009). Mathematics in India. Princeton: Princeton University Press. pp. 220, 319, 323. ISBN 9780691120676. Retrieved 7 April 2016.
3. ^ 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.