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What is the remainder?

  1. Jan 21, 2007 #1
    What is the remainder??

    1. The problem statement, all variables and given/known data

    What is the remainder when (a+b+c)^333-a^333-b^333-c^333 is divided by (a+b+c)^3-a^3-b^3-c^3?
    2. Relevant equations


    3. The attempt at a solution

    I tried this
    (a+b+c)^333-a^333-b^333-c^333 = Q{(a+b+c)^3-a^3-b^3-c^3}+h

    where h is the remainder
    I proceeded further but only managed to work out that Q>(a+b+c)^330.
    I don't know how to attack this types of problem.
    Please help!
  2. jcsd
  3. Jan 21, 2007 #2


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    Homework Helper

    Are these polynomials in the variables a,b,c? If so, I don't think there's a natural way to talk about remainders. You first have to define a norm on the set of polynomials. For example, you could take it to be the largest power of a (or b, or c, which is what I mean by when I say there's no natural way).
  4. Jan 21, 2007 #3

    Gib Z

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    Homework Helper

    Why Don't you just do it by hand? :p
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