Prove the following statement or give a counterexample.
If $d$ is any counting number and $d|b$, then there is a counting number $c$ such that $b=cd$.
This was my attempt at proving this. Am I on the right track?
Let $d|b$, then by quotient-remainder theorem: $$\frac bd= q=c \left[c=\frac bd\right]$$
The definition of $b\mid d$ is that there exists $k\in\Bbb{Z},$ so that $bk=d.$ Just use $c$ instead of $k.$