Section 1.1


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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