Let . Then .

This means

Now argue that is the least such exponent for .

The group has order . If you can show it is cyclic i.e. find a generator then by isomorphism proporties of cyclic groups it would mean that it has to be isomorphic to .(ii) prove that the direct sum of Zm and Zn is isomorphic to Zmn if and only if m and n are relatively prime.

any help would be appreciated. thanks