Exercise 2. This software determines when $$Z_n$$ is the only group of order $$n$$. Run the software for $$n = 105 = 3\times5\times7$$, $$165 = 3\times5\times11$$, $$195 = 3\times5\times13$$, $$255 = 3\times5\times17$$, $$345 = 3\times5\times23$$, $$435 = 3\times5\times29$$, $$385 = 5\times7\times11$$, $$455 = 5\times7\times13$$, $$595 = 5\times7\times17$$,$$1015 = 5\times7\times29$$, $$1085 = 5\times7\times31$$, and $$2415 = 3\times5\times7\times23$$. Conjecture a necessary and sufficient condition about $$n$$ for $$Z_n$$ to be the only group of order $$n$$.

Enter $$n$$, please enter $$105$$ instead of $$3\times5\times7$$ and click the button.