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Math Help - Rewording of a congruence class problem

  1. #1
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    Rewording of a congruence class problem

    If α is a quadratic integer in Q[√−d], then define a notion of congruence (mod α). Furthermore, define +, −, and for congruence classes, and show that this notion is well-defined.

    It's not that I don't know how to do this, I just don't understand what the question is asking. Can anyone rephrase this in simpler terms?
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  2. #2
    Senior Member roninpro's Avatar
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    The question is asking you to generalize the idea of congruence in \mathbb{Z}. That is, we write the congruence relation a\equiv b\pmod{n} if n divides a-b. Can you come up with a similar relation for \mathbb{Q}[\sqrt{d}]?
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  3. #3
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    Can we just define it in the same way? Let's define a, b, and c such that they are quadratic integers in the given field. If we have the proposition that a = b mod c, then how about we define that as c | (b - a), where the division results in a quadratic integer contained within the given ring of integers. That sounds pretty basic, am I overlooking something?
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