Two solutions of an equation of the form N·x² + k = y² in. Cross-multiply and recombine. Out comes a third solution to the same equation with a new additive. Brahmagupta wrote this composition rule down in 628 CE and called it bhāvanā — 'making right by combination.' It is the binary operation that turns a single seed solution into infinitely many, and the engine on which Bhāskara II's chakravala (1150 CE) was built to solve Pell's equation. Lagrange recovers the same composition structure independently in 1768.