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Math Help - Integer algebra

  1. #1
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    Integer algebra

    You choose three POSITIVE integers: x, y and z.
    The quotients 1. (x*y)/(x+y)
    2. (x*z)/(x+z)
    3. (y*z)/(y+z)
    shall also be integers.
    So, one has to prove the integers x, y and z have a factor in common which is bigger than 1.

    The problem is that I absolutely don't know how to prove this.
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  2. #2
    MHF Contributor kalagota's Avatar
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    x=y=z=2
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  3. #3
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    Well, 2 is a solution, but actually I do not have to point out a solution, but to prove that possible solutions have a factor bigger than 1 in common.
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