The Divisibility Relation.

Given integers \(m\) and \(n\text{,}\) we say “\(m\) divides \(n\)” and write

provided \(n \div m\) is an integer. Thus the following assertions mean the same thing:

1. \(\displaystyle m \mid n\)

2. \(n = mk\) for some integer \(k\)

3. \(m\) is a factor (or divisor) of \(n\)

4. \(n\) is a multiple of \(m\text{.}\)