brahmagupta's identity

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:

\left(a^2 + b^2\right)\left(c^2 + d^2\right) = \left(ac-bd\right)^2 + \left(ad+bc\right)^2.

The identity holds in any commutative ring, but most usefully in the integers. The identity was discovered by Brahmagupta (598-668), 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.

<< Previous

Word Browser

Next >>

eleonore louis godefroi cavaignac
finitely generated module
college of pontiffs
variety show
george francis (trainer)
lummi
yu gi oh!
george francis (robot wars)
mark fidrych
swinomish
el mariachi

guan dao
wb
swinomish (tribe)
tim skold
free module
symphony x
chicagoland
hoh
didache
manga entertainment
mathematics education

saline river (arkansas)
guan gong
serapion of antioch
irritation
charles o. finley
hyperbaric oxygen therapy
joshua chamberlain
bobby clarke
recluse spider
mokpo
pohang

anglo french condominium
karl richter
malcolm sargent
american express
giuseppe sinopoli
chuck brown
jinhae
korean national railroad
gunsan
geum river
iksan