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 $$n$$.