Section 1.1

# Introduction

Number theory is all about integers, primarily their properties under multiplication and addition. The cornerstone of the multiplicative theory is divisibility, so this first section is focused on giving a solid foundation on this topic.

As with most things mathematical, we'll start with a definition.

Definition: An integer a is said to divide another integer b if there exists an integer c such that b = ac. We write $a \mid b$ to mean “a divides b.”

The integer 9 divides the integer 18 because $18 = 9 \cdot 2.$
The integer 2 does not divide the integer 5 because it is impossible to find an integer c so that $5 = 2 \cdot c.$

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