Yes.

Yes.Secondly, since di | |(Z/nZ)*| = phi(n) for i=1,...,k am I correct in saying that L is less than or equal to phi(n)?

Yes, always.Main question(s):

When is phi(n)/L an integer (always?)?

No. If we could then we would have , a contradiction.More generally, can we write phi(n)/L as f(phi(n)) some function of phi(n)?

is an element of if and only if all of the following areWhen is phi(n) an element of (Z/nZ)*?false:

(1) for ;

(2) for some prime ;

(3) divides for some odd prime divisors of .

Cheers. Any help (on any of the questions) much appreciated.