Lagrange’s Four-square Theorem
mathematics
Lagrange’s four-square theorem, also called Lagrange’s theorem, in number theory, theorem that every positive integer can be expressed as the sum of the squares of four integers. For example,23 = 12 + 22 + 32 + 32. The four-square theorem was first proposed by the Greek mathematician Diophantus of Alexandria in his treatise Arithmetica (3rd century ce). Credit for the first proof is given to the 17th-century French amateur mathematician Pierre de Fermat. (Although he did not publish this proof, his study of Diophantus led to Fermat’s last theorem.) The first published proof of the four-square theorem was in 1770 by the French mathematician Joseph-Louis Lagrange, for whom the theorem is now named.
The impetus for renewed interest in Diophantus and such problems in number theory was the Frenchman Claude-Gaspar Bachet de Méziriac, whose Latin translation Diophanti (1621) of Arithmetica brought the work to a wider audience. In addition to the proof of Diophantus’s four-square theorem, study of the text led to a generalization of the theorem known as Waring’s problem.
What's Your Reaction?
![like](https://www.ridaxia.com/assets/img/reactions/like.png)
![dislike](https://www.ridaxia.com/assets/img/reactions/dislike.png)
![love](https://www.ridaxia.com/assets/img/reactions/love.png)
![funny](https://www.ridaxia.com/assets/img/reactions/funny.png)
![angry](https://www.ridaxia.com/assets/img/reactions/angry.png)
![sad](https://www.ridaxia.com/assets/img/reactions/sad.png)
![wow](https://www.ridaxia.com/assets/img/reactions/wow.png)