Brahmagupta's identity

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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.