NTIC Prologue

Chapter 1 Prologue

What is number theory? Briefly, it is the study of the integers and questions arising from them.

The set of counting numbers is denoted

$\begin{equation*} \mathbb{N} = \{0,1,2,3,4,\cdots\}\text{.} \end{equation*}$

Note that in this text, this set begins at zero. The integers is the set of positive and negative counting numbers:

$\begin{equation*} \mathbb{Z} = \{ \cdots ,-3,-2,-1,0,1,2,3,\cdots \}\text{.} \end{equation*}$

This is a fairly dry definition, though. The best way to find out what this definition means is to try to answer some questions about integers!