Exercise 3. In this exercise we assume \(a, b \in U(n)\). Define <\(a,b\)> \( = \{a^ib^j\; |\; 0 \leq i < |a|, 0 \leq j < |b|\}\). This software computes the orders of <\(a,b\)>, <\(a\)>, <\(b\)>, <\(a\)> \(\cap\) < \(b\)>. Run the program for the following choices for \(a, b\) and \(n\): (21, 101, 550), (21, 49, 550), (7, 11, 100) and (63, 77, 100). On the basis of the output, make a conjecture about arithmetic relationships among |<\(a,b\)>|, |<\(a\)>|, |<\(b\)>|, |<\(a\)> \(\cap\) < \(b\)>|.

Please enter \(a\), \(b\) and \(n\).

\(a\):
\(b\):
\(n\):