Home > Brahmagupta's identity

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:

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.