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.