$a, b, m$ are integers, such that $ab=m^2$
Prove that $a\over b$ and $b\over c$ are perfect squares, where $c$ is the GCF of $a$ and $b$.
I'm fairly new to mathematics and had never attempted to prove anything before. However, I did give this one a try and I'm hoping to receive constructive criticism, as well as other solutions to the problem(or, the correct solution, if mine is incorrect).
My solution goes as follows:
$ab$ can be represented as $m(m)$
Hence, $gcf(a,b) = c = gcf(m,m) = m$
Therefore, $\frac ac = \frac bc = \frac mm = 1$
$1$ can be represented as $1(1)$ and is a perfect square. I apologize if the formulation of my proposed proof is incorrect or difficult to understand. I'm still learning.