Exercise 1. This software computes the order of \(Aut(D_n)\). Run the program for \(n = 3, 5, 7, 11\). Make a conjecture about the order when n is prime. Run the program for \(n = 4, 8, 16, 32\). Make a conjecture when n is a power of 2. Run the program for \(n = 6, 10, 14, 22\). Make a conjecture when n is twice a prime. Run the program for \(n = 9, 15, 21, 33\). Make a conjecture when n is 3 times a prime. Try to deduce a general formula for the order of \(Aut(D_n)\).
Please enter \(n\), the result will show below.