Twenty-one algebraic normal forms of Citrabhānu (Q1386709)

The so-called ``normal forms of Citrabhānu'' (fl. ca. 1530) are rules for solving pairs of algebraic problems in two unknowns \(x\) and \(y\), where two given elements chosen among the following are given: the sum, or the difference, of \(x\) and \(y\), \(x^2\) and \(y^2\), or \(x^3\) and \(y^3\). This leads to 21 rules which are accompanied by examples and proofs, algebraic or geometrical. The author provides an exhaustive analysis of the subject together with a presentation of its historical development as found in earlier Sanskrit works by Brahmagupta and others.