Prove that if m is prime and m|kl then either m|k or m|l. Proofs homework question, here's what I've figured out thus far.
Suppose m doesn't divide k.  We need to then prove that m|l.  If m doesn't divide k and m is a prime then we know m and k are co-prime - hcf (m,k) = 1. Which means 1 = ks + mt  (for some integers; s,t).  
I'm not really sure where to go from here to prove that m|l based on these facts, help?

$$\frac\ell m=\frac{\ell\cdot1}m=\frac{\ell(ks+mt)}m=s\cdot\frac{k\ell}m+\ell t.$$Since $\ell,s,t$ are integers, and since $\frac{k\ell}m$ is an integer, it follows that $\frac\ell m$ is an integer, Q.E.D.
