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Discrete Math Proof

  1. Jul 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Let p(x) be a polynomial in F[x].

    Show that p1(x)≈p2(x) if and only if p(x)|(p1(x)-p2(x)) is an equivalence relation

    3. The attempt at a solution
    To be completely honest, I have no idea where to begin. This class has been a nightmare and this has been, by far, the worst professor I have ever had. No one in the class has any idea what is going on. I don't even really understand and to show the the second part of this is an equivalence relation.

    Thanks in advance for the help. I won't be offended if you speak to me like I'm a small child as I am so lost in this class.
  2. jcsd
  3. Jul 2, 2012 #2
    Well what are the three properties of an equivalence relation?
  4. Jul 2, 2012 #3
    In order for an equivalence relation to exist it must be symmetric, transitive and reflexive, but I don't know how to apply those.
  5. Jul 2, 2012 #4
    Start out with showing p1~p1... That is, p|(p1-p1)... p1~p2 => p|(p1-p2) => p|-(p2-p1) (assuming p=/=-1) => p|(p2-p1)
    Also p1~p2 and p2~p3.. What would p1-p2+(p2-p3) look like?
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