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 (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 |