1. The problem statement, all variables and given/known data Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in Z+ such that an=e. 2. Relevant equations a hint is given: consider e, a, a2,...am, where m is the number of elements in G, and use the cancellation laws. 3. The attempt at a solution so part of the trouble i'm having (i'm guessing the most important part), is figuring out what they're asking. is the number n i'm looking for a number that when any a in G is raised to, it gives the identity? i.e. (i'm just picking random letters) an= e and bn=e when a and b are not equal but n is the same in both? i was working on this question for a while thinking it to mean that a particular ap might have n0 while aq might have n1 to take it to e (identity).