Thread: 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

Originally Posted by scottie.mcdonald

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 ?

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