Definition#

Let \(a\) and \(b\) be integers. We say that \(a\) divides \(b\) (or \(b\) is a multiple of \(a\)) if there exists an integer \(c\) such that \(b=ac\). In this case, we write \(a \mid b\).

Example#

As \(84 = 6(14)\) and \(84 = -3(-28)\), we write \(6 \mid 84\) and \(-3 \mid 84\). On the other hand, \(10 \nmid 84\).

Source#

Gregory T. Lee. Abstract Algebra. 1st ed. Springer Cham, 2018. pp. 20.