This software computes the order of
.
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
.
(Please install java SDK or JDK on your computer if you could not see the program below.) |