Editing Lagrange's four-square theorem (section)

==Historical development==
From examples given in the ''[[Arithmetica]],'' it is clear that [[Diophantus]] was aware of the theorem. This book was translated in 1621 into Latin by [[Claude Gaspard Bachet de Méziriac|Bachet (Claude Gaspard Bachet de Méziriac)]], who stated the theorem in the notes of his translation. But the theorem was not proved until 1770 by Lagrange.<ref>{{harvnb|Ireland|Rosen|1990}}.</ref>

[[Adrien-Marie Legendre]] extended the theorem in 1797–8 with his [[Legendre's three-square theorem|three-square theorem]], by proving that a positive integer can be expressed as the sum of three squares if and only if it is not of the form <math>4^k(8m+7)</math> for integers {{mvar|k}} and {{mvar|m}}. Later, in 1834, [[Carl Gustav Jakob Jacobi]] discovered a simple formula for the number of representations of an integer as the sum of four squares with his own [[Jacobi's four-square theorem|four-square theorem]].

The formula is also linked to [[Descartes' theorem]] of four "kissing circles", which involves the sum of the squares of the curvatures of four circles. This is also linked to [[Apollonian gasket]]s, which were more recently related to the [[Ramanujan–Petersson conjecture]].<ref>{{harvnb|Sarnak|2013}}.</ref>