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Math Help - Equivalence Relations help needed

  1. #1
    Junior Member scottie.mcdonald's Avatar
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    Equivalence Relations help needed

    The question:

    Let A=integers and, for all m,nE integers, define mRn <=> ((m^2)-(n^2)).
    What is the equivalence class of 1? Describe all distinct equivalence classes.

    Here's what I have so far:

    [1]={mE integers : mR0}
    ={mE integers : 3|m^2}
    ={mE integers : 3a=m^2 for some aE integers}
    ={mE integers : square root(3a)=m}

    note: <=> represents if and only if and 3|m^2 is read as 3 divides m squared

    I believe that I have up to the second line correct, but after that I
    am confused on what to do. I've also tried using actual numbers to get a sense of what's going on, but I don't think the root(3a)=m is correct.

    Any help would be nice. Thank you
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  2. #2
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    Quote Originally Posted by scottie.mcdonald View Post
    The question:
    Let A=integers and, for all m,nE integers, define mRn <=> ((m^2)-(n^2)).
    What is the equivalence class of 1? Describe all distinct equivalence classes.
    That is not an equivalence relation!
    Did you mean m^2 = n^2?
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  3. #3
    Junior Member scottie.mcdonald's Avatar
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    sorry, left out part of the equation (oops).

    should read:

    Let A=integers and, for all m,nE integers, define mRn <=> 3|((m^2)-(n^2)).........

    where 3| means 3 divides m squared - n squared
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