Brahmagupta-Fibonacci identity

See in particular the Brahmagupta-Fibonacci identity.

The Brahmagupta-Fibonacci identity says the set of all sums of two squares is closed under multiplication.

The Brahmagupta-Fibonacci identity states that the product of two sums of two squares is a sum of two squares.

(known as the Brahmagupta-Fibonacci identity), and also Euler's four-square identity and Degen's eight-square identity.

In algebra, the Brahmagupta-Fibonacci identity or simply Fibonacci's identity (and in fact due to Diophantus of Alexandria) says that the product of two sums each of two squares is itself a sum of two squares.