# Brahmagupta's identity

In

mathematics,

**Brahmagupta's identity** says that the product of two numbers, each of which being 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.

See also Euler's four-square identity. There is a similar eight-square identity derived from the Cayley numbers, but that isn't particularly interesting for integers because every positive integer is a sum of four squares.