Proof of Even/Odd Case for a|bc in Z: Does a|b or a|c?

[John112]

$\forall$ a,b,c $\in$ $Z$ a|bc $\Rightarrow$ a|b or a|c

To prove this do I only need to show that 'a' can be either even or odd?

 

[Dick]

$\forall$ a,b,c $\in$ $Z$ a|bc $\Rightarrow$ a|b or a|c

To prove this do I only need to show that 'a' can be either even or odd?

You can't prove it because it isn't true. Find a counterexample.