Here is what I am trying to prove:
Let $a,b,c,d \in ℤ_+$ with gcd$(a,b)=1$. If $a|c$ and $b|c$, prove that $ab|c$. Does the result hold if gcd $(a,b)\neq 1$ ?
I know that gcd $(a,b)=1$ can be written $ax+by=1$ where $x,y$ are integers. And $a|c$ can be written $c=al$ where $l$ is an integer, b|c can be written $c=bk$ where $k$ is an integer, and $ab|c$ can be written $c=ab(m)$ where $m$ is an integer.
What do I do?