Okay, I wasn't sure where to post this, because it involves number theory, but since I am asking a question about probabilities, and I think it is fairly simple (I am not a star in prob's), I guess it belongs here.

Say we have the progression :

With a composite number (for instance ), and a a positive integer in

Question: what is the probability that a number picked at random in its interval generates a sequence in which , with , shares a common factor with ? You may express your answer in terms of , , and (where is the n'th prime factor of )

I am really stumped on this question, there is a lot of information and I don't know where to start. I think it might be useful to use the prime factors of , but I just don't know where to start the answer .

Thanks a lot !