Editing Algebraic number theory (section)

===Diophantus===
The beginnings of algebraic number theory can be traced to Diophantine equations,<ref>Stark, pp. 145–146.</ref> named after the 3rd-century [[Alexandria]]n mathematician, [[Diophantus]], who studied them and developed methods for the solution of some kinds of Diophantine equations. A typical Diophantine problem is to find two integers ''x'' and ''y'' such that their sum, and the sum of their squares, equal two given numbers ''A'' and ''B'', respectively:

:<math>A = x + y\ </math>
:<math>B = x^2 + y^2.\ </math>

Diophantine equations have been studied for thousands of years. For example, the solutions to the quadratic Diophantine equation <br /> ''x''<sup>2</sup> + ''y''<sup>2</sup> = ''z''<sup>2</sup> are given by the [[Pythagorean triple]]s, originally solved by the Babylonians ({{circa|1800 BC}}).<ref>Aczel, pp. 14–15.</ref> Solutions to linear Diophantine equations, such as 26''x'' + 65''y'' = 13, may be found using the [[Euclidean algorithm]] (c. 5th century BC).<ref>Stark, pp. 44–47.</ref>

Diophantus's major work was the ''[[Arithmetica]]'', of which only a portion has survived.