So I am working on a proof where I end up with $17|nq$ where $n$ is a natural number and $q$ is an integer. I want to show $q$ is divisible by 17 for all $n$ and $q$. I think I can prove the statement once I know what $17|nq$ implies in terms of possible cases and how I can get to $17|q$
short part from the proof: By lemma $\omega$, since $17|(nq)^2$, $17|nq$ thus we can express $nq$ as $nq=17 \tau$ with $\tau \in \mathbb{Z}$