Editing Diophantus (section)

===Contents===
In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form <math>4n + 3</math> cannot be the sum of two squares. Diophantus also appears to know that [[Lagrange's four-square theorem|every number can be written as the sum of four squares]]. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his doing so would be truly remarkable:  even Fermat, who stated the result, failed to provide a proof of it and it was not settled until [[Joseph-Louis Lagrange]] proved it using results due to [[Leonhard Euler]].