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- Legendre's_three-square_theorem abstract "In mathematics, Legendre's three-square theorem states that any natural number that is not of the form for integers a and b can be represented as the sum of three integer squares:This theorem was stated by Adrien-Marie Legendre in 1798. His proof was incomplete, leaving a gap which was later filled by Carl Friedrich Gauss.This theorem leads to an easy proof of Lagrange's four-square theorem, which states that all natural numbers can be written as a sum of four squares. Let n be a natural number, then there are two cases: either n is not of the form , in which case it is a sum of three squares and thus of four squares for some x, y, z, by Legendre–Gauss; or , where , which is again a sum of three squares by Legendre–Gauss, so that n is a sum of four squares.".
- Legendre's_three-square_theorem wikiPageID "40708124".
- Legendre's_three-square_theorem wikiPageRevisionID "599569146".
- Legendre's_three-square_theorem subject Category:Additive_number_theory.
- Legendre's_three-square_theorem subject Category:Theorems_in_number_theory.
- Legendre's_three-square_theorem comment "In mathematics, Legendre's three-square theorem states that any natural number that is not of the form for integers a and b can be represented as the sum of three integer squares:This theorem was stated by Adrien-Marie Legendre in 1798. His proof was incomplete, leaving a gap which was later filled by Carl Friedrich Gauss.This theorem leads to an easy proof of Lagrange's four-square theorem, which states that all natural numbers can be written as a sum of four squares.".
- Legendre's_three-square_theorem label "Legendre's three-square theorem".
- Legendre's_three-square_theorem label "Théorème des trois carrés".
- Legendre's_three-square_theorem sameAs Théorème_des_trois_carrés.
- Legendre's_three-square_theorem sameAs m.0y4wpxy.
- Legendre's_three-square_theorem sameAs Q15940470.
- Legendre's_three-square_theorem sameAs Q15940470.
- Legendre's_three-square_theorem wasDerivedFrom Legendre's_three-square_theorem?oldid=599569146.
- Legendre's_three-square_theorem isPrimaryTopicOf Legendre's_three-square_theorem.