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Math Help - hello~

  1. #1
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    Sep 2009
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    hello~

    anybody try solve this problem:
    find all triples of positive integers(x,y,z) such that
    x*y*z+x*y+y*z+z*x+x+y+z=243
    tq
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    xyz+xy+xz+yz+x+y+z=(x+1)(y+1)(z+1)-1=243

    so (x+1)(y+1)(z+1)=244=2^2\cdot 61

    so we must have x=1,y=1,z=60.

    Nice problem!
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