Brahmagupta's identity
From Academic Kids
In mathematics, Brahmagupta's identity says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares. Specifically:
- <math>\left(a^2 + b^2\right)\left(c^2 + d^2\right) = \left(ac-bd\right)^2 + \left(ad+bc\right)^2.<math>
The identity holds in any commutative ring, but most usefully in the integers.
The identity was discovered by Brahmagupta (598-668), an Indian mathematician and astronomer.
See also Euler's four-square identity. There is a similar eight-square identity derived from the Cayley numbers, but it isn't particularly interesting for integers because every positive integer is a sum of four squares.es:Identidad de Brahmagupta fr:Identité de Brahmagupta it:Identità di Fibonacci sl:Brahmaguptina enakost
