**Exercise 1.**
This software determines the homomorphisms from \(Z_m\) to \(Z_n\). (Recall that a homomorphism from \(Z_m\) 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 \(Z_m\) to \(Z_n\)? 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 \(n\).

Please enter \(m\) and \(n\).