This software determines the homomorphisms from Zm to Zn.
Chapter 10, Problem 1CE(choose chapter or problem)
This software determines the homomorphisms from Zm to Zn. (Recall that a homomorphism from Zm is completely determined by the image of 1.) Run the program for m = 20 with various choices for n. Run the program for m = 15 with various choices for n. What relationship do you see between m and n and the number of homomorphisms from Zm to Zn? For each choice of m and n, observe the smallest positive image of 1. Try to see the relationship between this image and the values of m and n. What relationship do you see between the smallest positive image of 1 and the other images of 1? Test your conclusions with other choices of m and n.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer