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.
\(n\):