# 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 |