Simple Division Proof

Question

Prove that for every three integers i, j, and k, if i $\nmid$ jk, then i $\nmid$ j

We've just started proofs and I am at a complete loss for how to go about doing it. I've tried proving through contradiction by assuming that it is divisible but I have gotten no where.

Any help would be greatly appreciated

Answer 1

If $i$ divides $j$ then $j=id$ for some integer $d$. Then, $i(dk)=(id)k=jk$, so $i$ divides $jk$.

Answer 2

If $i|j$ then $iq=j$ for some $q$ hence $jk=(iq)k=i(qk)$ therefore $i|jk$ which contradicts our initial assumption.