Chapter 24 Exercise 2

This software determines when Zn is the only group of order n.

Run the software for n = 105 = 3*5*7, 165 = 3*5*11, 195 = 3*5*13, 255 = 3*5*17, 345 = 3*5*23,
435 = 3*5*29, 385 = 5*7*11, 455 = 5*7*13, 595 = 5*7*17, 1015 = 5*7*29, 1085 = 5*7*31,
and 2415 = 3*5*7*23.

Conjecture a necessary and sufficient condition about n for Zn to be the only group of order n.
(Please install java SDK or JDK on your computer if you could not see the program below.)
(Please enter 105 instead of 3*5*7)