## Abstract

The theory of numbers is concerned with the properties of the **integers**, that is, the class of whole numbers and zero, 0, ±1,±2 .... We will denote the class of integers by ℤ. The positive integers, 1, 2, 3..., are called the **natural numbers**, which we will denote by ℕ. We will assume that the reader is familiar with the basic arithmetic properties of ℤ, and in this section we will look at the abstract algebraic properties of the integers and what makes ℤ unique as an algebraic structure.

## Keywords

Integral Domain Residue Class Primitive Root Chinese Remainder Theorem Multiplicative Inverse
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Birkhäuser Boston 2007