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Diophantus

The beginnings of algebraic number theory can be traced to Diophantine equations, named after the 3rd-century Alexandrian 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:

Diophantine equations have been studied for thousands of years. For example, the solutions to the quadratic Diophantine equation x + y = z are given by the Pythagorean triples, originally solved by the Babylonians (c. 1800 BC). Solutions to linear Diophantine equations, such as 26 x + 65 y = 13, may be found using the Euclidean algorithm (c. 5th century BC).

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