In mathematics, Brahmagupta's identity says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares. Specifically: Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction. ...

The identity holds in any commutative ring, but most usefully in the integers. In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law. ... The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ...

The identity was discovered by Brahmagupta (598-668), an Indian mathematician and astronomer. Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ...

See also Euler's four-square identity. There is a similar eight-square identity derived from the Cayley numbers, but it isn't particularly interesting for integers because every positive integer is a sum of four squares. In mathematics, Eulers 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. ... In mathematics, the octonions are a nonassociative extension of the quaternions. ... Lagranges four-square theorem, also known as Bachets Conjecture, was proved in 1770 by Joseph Louis Lagrange. ...