
Congruence Classes
Hello all!
I was looking over some examples of congruence classes and I ran into one I could not find.
1. Is there/Are there a congruence class(es) $\displaystyle (mod (3+\sqrt{3})/2) $ in $\displaystyle Q[\sqrt{3}] $ ? If so, what are they? I'm not sure if they exist or not even.
2. If $\displaystyle \alpha $ is a quadratic integer in $\displaystyle Q[\sqrt{d}] $, then a notion of congruence $\displaystyle (mod \alpha) $ can be defined. How can this be defined how can we further define +, , and x for congruences classes?
Thank you everyone!
Samson

What in the world. In one of your past posts, specifically this one:
http://www.mathhelpforum.com/mathhe...rs154495.html
You clearly state that you know the congruence classes are 1, 0, and 1. And in this post, you're asking what the congruence classes are. This doesn't make any sense, what's going on?
By the way, the congruence classes are 1, 0, and 1, which you seemed to know earlier but not now.