In mathematics, **Euler's four-square identity** says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically:

*a*s and

*b*s are real numbers, a more elegant proof is available: the identity expresses the fact that the absolute value of the product of two quaternions is equal to the product of their absolute values, in the same way that Brahmagupta's identity does for complex numbers.

The identity was used by Lagrange to prove his four square theorem.