be a group. [tex]a,b /in G[\math]
Prove there exists an element in with order = LCM . Let this LCM be
Let order of be
Obviously (as )
Only two cases are possible
Case 1: AND - we are done here
Case 2: doesn't divide AND doesn't divide
In this case we have = where and
Stuck here for quite some time.
Is my approach correct? If yes, hint on way fwd please?