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Homework Help: Proof: (Pigeon Hole Principle) from a Problem Solving Class

  1. Jan 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that THEIR EXISTS INTEGERS a,b,c NOT ALL 0 AND EACH OF ABSOLUTE VALUE <10^6 SUCH THAT
    |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11


    2. Relevant equations


    |a + sqrt(2)*b + cuberoot(3)*c| < 10^-11


    3. The attempt at a solution

    Well, I know that we have to use the pigeon hole principle, otherwise I am completely lost.

    I did try to actually find values for a,b,c ... but no luck with that.

    I am now attempting to rearrange the formula and solve for some variable in terms of another.

    Has anybody seen a problem like this before? Does it have a name?
     
  2. jcsd
  3. Jan 13, 2007 #2
    Never mind people, after a lot of hard thinking, i got it (well...close to it!)
     
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