I don't think you need the modulus stuff in this problem. Focus on what the basic terminology means; e.g., a | bc means that bc = k*a for some integer k, and what it means for two integers to be relatively prime.
It might be helpful to cook up a few examples using numbers. These won't do for a proof, but it might help you get some better understanding of how the proof would need to go.
1. Let a = 5 and b = 9, and let c = 6
Here a and b are relatively prime, and c > =
Does 5 | 54 ? No. Do we need to show that 5 | 6? No, since the condition that a | bc isn't met.
2. Let a = 5 and b = 9, as before, and let c = 8
Does 5 | 72? No. Do we need to show that 5 | 8? No, since the condition that a | bc isn't met.
3. Let a = 5 and b = 9, as before, and let c = 10
Does 5 | 90? Yes. Does 5 | 10? Yes.
rooski said:
what bothers me most about these proofs is that there's no set method for solving them, you're just supposed to somehow come up with a solution out of thin air. :S
Proofs involve a different way of thinking than you are probably used to, so in one respect, they are harder. On the other hand, you know what the answer is, and it's just a matter of getting to it!