Test if equation allows integer variables

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Sorry it can be silly but i am stuck and can't get my head around this.

I have an equation like;

$b = \frac{qc}{p} + \frac{p}{2}$

Now $p$ and $q$ are known integer values whereas $b$ and $c$ are the variables. How can I test on $p$ and $q$ that the equation allows integer $b$ and $c$?