# 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 LagrangesFoursquareTheorem 2013-03-22 12:35:17 2013-03-22 12:35:17 bbukh (348) bbukh (348) 10 bbukh (348) Theorem msc 11P05 WaringsProblem EulerFourSquareIdentity