Proof

Suppose \(a \mid b\text{.}\) Then \(b\) is a multiple of \(a\text{,}\) or in other words, \(b = ak\) for some \(k\text{.}\) But then \(bc = akc\text{,}\) and since \(kc\) is an integer, this says \(bc\) is a multiple of \(a\text{.}\) In other words, \(a \mid bc\text{.}\)