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Number theory is a broad and diverse part of mathematics that developed from the study of the **integers**. In this article we describe two kinds of problems that have stimulated the development of number theory.

A very old problem in number theory is to determine the integer solutions to **equations** or systems of simultaneous equation. Equations to be solved in integers are called *Diophantine equations* after **Diophantus of Alexandria**. Diophantus probably lived about 250 a.d. He is known for his work *Arithmetica* in which he posed and solved various types of equations in integers. This part of number theory has strong connections to **algebraic geometry** and is sometimes referred to as *Diophantine geometry*. In some cases it is possible to completely determine all integer solutions to a particular Diophantine equation. For example, it is possible to describe all of the triples of integers (*x, y, z...*

This section contains 898 words(approx. 3 pages at 300 words per page) |