Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers. Form the assumption, we can say $b=ak$ ,$k$ integer, $a=bm$, $m$ integer.
 Intuitively, this conjecture makes sense. But I can't make further step.

$$a /b$$ then $$|a| \le |b|$$
$$b / a $$ then $$ |b| \le |a|$$
thus
$$|a| = |b|$$
