In case the symbols aren't clear, , ie. residue classes mod 36. This one is written multiplicatively while is written additively.Let . For which does the map extend to a well defined homomorphism? Can ever be a surjective homomorphism?

I handled the a part of the question: all a such that (a, 36) = 1 will do the trick.

But isn't already a surjective homomorphism? Or am I supposed to show the modular nature of the problem creates the surjection?

Thanks!

-Dan