I'm learning about properties of greatest common divisors, specifically when two numbers are relatively prime.
The exercise I'm working through is :
Suppose that $\gcd(a,b) = 1$ and that $a\mid n$ and $b\mid n$. Prove that $ab\mid n$
$\gcd(a,b)=1$ implies $am+bk = 1$ for some integers $m$ and $k$.
(Given hint) Multiplying the equation by $n$ yields: $$amn+bkn=n$$
I'm not sure what to do after applying the hint. Am I supposed to show that $ab$ divides both $amn$ and $bkn$?
Thanks in advance.