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 4n(8m+7) require four squares.

This shows that g(2)=G(2)=4, where g and G are the Waring functions (

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