Problem Statement:

For each integer , define by

Let

Prove that is cyclic. (Indicate a generator of ).

Attempt at a solution (brainstorming of where to begin):

I know that all subsets of can be generated by 1 under modulo addition (except, zero, right?). Also, I believe it is true that the can be generated by under modulo additon (I think I read that on the internet somewhere, so it must be true).

My inclanation is to go the modulo addition route. However, I'm getting hung up on the . If is some arbitrary element, then could very well be irrational, correct? In which case, does modulo addition even work with non-integers? When considering , do I take to be a fixed element?

Is this one one those cases where I'm going to have to make some assumptions about in my proof? For example say something like "Suppose ..."

Or maybe I don't even need to go the modulo addition route at all? Should I be working a different angle?

Any hints on where to start on this, would be awesome!

Thanks!