It seems to me that |U(r)| x |U(s)| x gcd(r,s) = |U(rs)|. All of the integers in Problem 38 had a gcd of 1, but 4 and 10 have a gcd of 2. I thought of a couple other examples that this works for (2 and 4 is a simple example that holds).
-DK
I thought that if Let U(r)=a U(s)=b if either one or both r or s is prime then |U(rs)|=2*(ab). Same thing you have but said differently Jenny
