I know that the question doesn't really match the level of this site, but I will be very grateful if someone showed me the proof:
$\forall x,y,z \in \mathbb{Z}$ if $xz \hspace{4 pt} \vdots \hspace{4 pt} (z - y)$ then $xy \hspace{4 pt} \vdots \hspace{4 pt} (z - y)$,
When $x \hspace{4 pt} \vdots \hspace{4 pt} (z - y)$, it's obvious that for any $y \in \mathbb{Z}$ this holds. But how do I prove for all the other cases?
Thank you!