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.