# Congruence Classes

• Oct 9th 2010, 06:11 PM
Samson
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) $(mod (3+\sqrt{3})/2)$ in $Q[\sqrt{-3}]$ ? If so, what are they? I'm not sure if they exist or not even.

2. If $\alpha$ is a quadratic integer in $Q[\sqrt{-d}]$, then a notion of congruence $(mod \alpha)$ can be defined. How can this be defined how can we further define +, -, and x for congruences classes?

Thank you everyone!

-Samson
• Nov 28th 2010, 10:34 AM
elemental
What in the world. In one of your past posts, specifically this one:
http://www.mathhelpforum.com/math-he...rs-154495.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.