Editing Number theory (section)

===== Late Antiquity =====
[[File:Diophantus-cover.png|thumb|upright=0.8|Title page of Diophantus's ''{{lang|la|[[Arithmetica]]}}'', translated into Latin by [[Claude Gaspard Bachet de Méziriac|Bachet]] (1621)]]

Aside from the elementary work of Neopythagoreans such as [[Nicomachus]] and [[Theon of Smyrna]], the foremost authority in {{tlit|grc|arithmētikḗ}} in Late Antiquity was [[Diophantus of Alexandria]], who probably lived in the 3rd century&nbsp;AD, approximately five hundred years after Euclid. Little is known about his life, but he wrote two works that are extant: ''On Polygonal Numbers'', a short treatise written in the Euclidean manner on the subject, and the ''[[Arithmetica]]'', a work on pre-modern algebra (namely, the use of algebra to solve numerical problems). Six out of the thirteen books of Diophantus's ''Arithmetica'' survive in the original Greek and four more survive in an Arabic translation. The ''{{lang|la|Arithmetica}}'' is a collection of worked-out problems where the task is invariably to find rational solutions to a system of polynomial equations, usually of the form <math>f(x,y)=z^2</math> or <math>f(x,y,z)=w^2</math>. In modern parlance, [[Diophantine equation]]s are [[polynomial equation]]s to which rational or integer solutions are sought.