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How to solve it

  1. Mar 27, 2005 #1
    "Find a positive integer 'm' such that m/2 is a perfect square and m/3 is a perfect cube."

    How to solve it?
     
  2. jcsd
  3. Mar 27, 2005 #2

    matt grime

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    consider m's prime decomposition
     
  4. Mar 27, 2005 #3

    dextercioby

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    The smallest one can find is

    [tex] M=3^{4}\cdot 2^{3}=648 [/tex]

    Daniel.
     
  5. Mar 27, 2005 #4
    Prime factorization::thanks

    Now just one more question: Is it impossible to construct an equilateral triangle using only lattice points?---(i.e., points with integer coordinates)
    My work says no---but can it be done?
     
  6. Mar 27, 2005 #5

    dextercioby

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    Nope,if one of the sides is || with one of the axis of coordinates...The height of the triangle is

    [tex] h=\frac{l\sqrt{3}}{2} [/tex]...(that justifies it)...

    As for the general case,it is a system of 3 equations with 6 unknowns...

    Daniel.
     
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