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Homework Help: Sum of 2 cubes ?

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data
    1729 is the smallest positive integer that can be represented in two different ways as the sum of two cubes , what are the two ways.
    They have to be natural numbers.
    3. The attempt at a solution

    x^3+Y^3=1729 i could just find the answer by guess and check , but im not sure how to do it analytically.
  2. jcsd
  3. May 24, 2010 #2


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    You can simplify a little by using [itex]x^3+ y^3= (x+ y)(x^2- xy+ y^2)[/itex].

    Now, factor 1729 to find two factors that would fit that.
  4. May 24, 2010 #3
    sweet thanks for the help
  5. May 25, 2010 #4


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    I remember my teacher showing us a method with complex numbers and moduli to find the sum of two squares to equal some number we have. If only I remember the method... Maybe this can be extended to the sum of two cubes?
  6. May 26, 2010 #5


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    You can't not know the oft-told tale about this question and this number?
  7. May 26, 2010 #6


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    There is a very oft-told tale about this question with this number many people here will know.
    Last edited: May 26, 2010
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