Brahmagupta–Fibonacci identity

In algebra, the Diophantus–Fibonacci identity, 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. In other words, the set of all sums of two squares is closed under multiplication. Specifically:

Brahmagupta-Fibonacci identity — ${\displaystyle {\begin{aligned}\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)&{}=\left(ac-bd\right)^{2}+\left(ad+bc\right)^{2}&&&(1)\\&{}=\left(ac+bd\right)^{2}+\left(ad-bc\right)^{2}.&&&(2)\end{aligned}}}$

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