About: Lagrange's four-square theorem

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Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. where the four numbers are integers. For illustration, 3, 31, and 310 in several ways, can be represented as the sum of four squares as follows: This theorem was proven by Joseph Louis Lagrange in 1770. It is a special case of the Fermat polygonal number theorem.

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rdf:type	Thing
rdfs:label	Lagrange's four-square theorem (en)
rdfs:comment	Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. where the four numbers are integers. For illustration, 3, 31, and 310 in several ways, can be represented as the sum of four squares as follows: This theorem was proven by Joseph Louis Lagrange in 1770. It is a special case of the Fermat polygonal number theorem. (en)
sameAs	Lagrange's four-square theorem Lagrange's four-square theorem
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Subject	Additive number theory Articles containing proofs Squares in number theory Theorems in number theory
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Wikipage page ID	326395 (xsd:integer)
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Wikipage revision ID	1070361127 (xsd:integer)
Link from a Wikipage to another Wikipage	Proof by infinite descent Sum of squares function Sum of two squares theorem Sun Zhiwei Unique factorization domain Wiley (publisher) 15 and 290 theorems Additive basis Adrien-Marie Legendre Apollonian gasket Arithmetica Cambridge University Press Carl Gustav Jacob Jacobi Additive number theory Articles containing proofs Squares in number theory Theorems in number theory Jacobi's four-square theorem Joseph-Louis Lagrange Diophantus Divisor Divisor function Jeffrey Shallit Legendre's three-square theorem Pigeonhole principle Quaternion Claude Gaspar Bachet de Méziriac Hurwitz quaternion Prime number Principal ideal Square number Srinivasa Ramanujan Time complexity Michael O. Rabin Waring's problem Finite field Ideal (ring theory) Descartes' theorem Thue's lemma Fermat polygonal number theorem Field norm Half-integer Integer Irreducible element Lagrange's theorem (number theory) Modular arithmetic Euclidean domain Euler's four-square identity History of numbers Ramanujan–Petersson conjecture Randomized algorithm Rational number Ring (mathematics)
has abstract	Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. where the four numbers are integers. For illustration, 3, 31, and 310 in several ways, can be represented as the sum of four squares as follows: This theorem was proven by Joseph Louis Lagrange in 1770. It is a special case of the Fermat polygonal number theorem. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
is Wikipage redirect of	Bachet's conjecture Bachet's theorem Bachet conjecture Bachet theorem Lagrange's 4-square theorem Lagrange four-square theorem Pythagorean quintuple Sum of four squares Four-square theorem Four square theorem Four squares theorem 4 square theorem
is Link from a Wikipage to another Wikipage of	Four square (disambiguation) List of theorems List of things named after Joseph-Louis Lagrange Number theory

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