Editing Quaternion (section)

== Lagrange's four-square theorem ==
{{Main|Lagrange's four-square theorem}}
Quaternions are also used in one of the proofs of Lagrange's four-square theorem in [[number theory]], which states that every nonnegative integer is the sum of four integer squares. As well as being an elegant theorem in its own right, Lagrange's four square theorem has useful applications in areas of mathematics outside number theory, such as [[combinatorial design]] theory. The quaternion-based proof uses [[Hurwitz quaternion]]s, a subring of the ring of all quaternions for which there is an analog of the [[Euclidean algorithm]].