(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm starting an introductory course in "Advanced math" and need a little homework guidance please.

The question: Let a, b, and q be natural numbers, and q > 1. Prove that if q has the property: q divides a or q divides b whenever q divides ab, then q is prime.

2. Relevant equations

3. The attempt at a solution

Ok. First I'm assuming that this proof can't be too hard especially for one of the first assignments and is probably a standard one to assign new students in this subject so I apologize if this has been asked before. A little nudge in the right direction would be helpful. I think that I should try to prove the contrapositive. So assume q is not prime but then I am a little confused on what exactly ~(p) would be. Any help would be appreciated

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# Homework Help: Prime number proof

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