Lagrange’s four-square theorem

Lagrange’s four-square theorem states that every non-negative integer may be expressed as the sum of at most four squares. By the Euler four-square identity, it is enough to show that every prime is expressible by at most four squares. It was later proved that only the numbers of the form $4^n(8m+7)$ require four squares.

This shows that $g(2)=G(2)=4$, where $g$ and $G$ are the Waring functions (http://planetmath.org/WaringsProblem).

Title	Lagrange’s four-square theorem
Canonical name	LagrangesFoursquareTheorem
Date of creation	2013-03-22 12:35:17
Last modified on	2013-03-22 12:35:17
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	10
Author	bbukh (348)
Entry type	Theorem
Classification	msc 11P05
Related topic	WaringsProblem
Related topic	EulerFourSquareIdentity