Originally Posted by

**mdoyle** Ok, I figured out [x] (it's the congruence class of x, yay!), but I'm given that the mapping in my first post is a homomorphism and I'm told to prove it. In order to prove that, I would have to show [x + y] = [x] + [y].

I don't see how that is true; for mod 3, [0] = {..., -6, -3, 0, 3, 6, ...} and

[1] = {..., -5, -2, 1, 4, 7, ...}. According to that equation, [0 + 1] = [0] + [1] = {..., -11, -5, 1, 7, 13, ...} which would be [1] with respect to mod 6.

Am I on the right track here, or am I completely off?