<p>I have a hard time following your argument in its continuing forms. You are misunderstanding my reasoning, and if not, you are misrepresenting it. </p>
<p>It really is not that complicated. While the factors of 12 could be 3 and 4, the only factor that is relevant for for p-n is 4 per the problem statement. Since p+n has to be larger than p-n, it cannot be smaller than 4. Accordingly, 3*4 is NOT a possible solution. It is totally irrelevant to define p or n.</p>