If \(a|b\) and \(c|d\), then there are integers \(e\) and \(f\), such that \(ae = b\) and \(cf = d\). That means:
\[bd = (ae) * (cf) = (ac)*(ef)\]
In other words:
\[bd = (ac)*k\]
where \(k \in ℤ\). This shows that \(ac|bd\).
If \(a|b\) and \(c|d\), then there are integers \(e\) and \(f\), such that \(ae = b\) and \(cf = d\). That means:
In other words:
where \(k \in ℤ\). This shows that \(ac|bd\).