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Chapter1Prologue

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

Definition1.0.1

The set of counting numbers is denoted \begin{equation*}\mathbb{N} = \{0,1,2,3,4,\cdots\}\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 \}\end{equation*}

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