1. The problem statement, all variables and given/known data Is the group of positive rational numbers under multiplication a cyclic group. 2. Relevant equations 3. The attempt at a solution So a group is cyclic if and only if there exists a element in G that generates all of the elements in G. So the set of positive rational numbers would be cyclic if we could find a fraction a/b such that (a/b)^n, where n is an integer, generates all elements of positive Q. I feel like the group is not cyclic, which means that I would have to prove that for all elements in positive Q, they don't generate positive Q. I am not sure exactly how to approach this... For (a/b)^n, do I have to find another fraction in terms of a and b such that (a/b)^n can't equal that expression for any n?