I came accross this question. Is the group (ℤ/34/ℤ)x cyclic? We haven't discussed the theorem in class that any units group of Z modulo n is iff n = 1, 2, 4, pk and 2pk (where p is an odd prime). But thanks to Deveno I know about it. So in this case, p =17 works, so the group is cyclic? but is there a different way to show it besides using brute force .