Chakravala method for Pell equation
Método chakravala para la ecuación de Pell
- Date
- 1150 · confidence high
- Place
- Ujjain, India
- Credited to
- Bhaskara II (Bijaganita); earlier work by Jayadeva and Brahmagupta
- People
- 👤 Bhaskara II1114–1185
- Field
- Knowledge & symbols
What was discovered
A cyclic algorithm that finds integer solutions of x^2 - Ny^2 = 1, solving, for instance, N = 61 with nine-digit numbers. Bhaskara also dealt with derivatives of sines and an embryonic form of Rolle's theorem.
In 1657 Fermat proposed the case N = 61 as a challenge without knowing of the Indian solution; the name Pell is a mistake by Euler.
What it led to
- continued fractions
- algebraic number theory
- units of quadratic fields
Built on
- Kuttaka: solving linear Diophantine equations499
- Brahmagupta's composition identity (bhavana)628
- Brahmagupta (composition identity)