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Factoring Help

  1. Feb 24, 2013 #1
    Hey everyone first time poster here, I need help with some factoring of cubes. I know this might tie closely to Diophantine equations but here goes.

    Under what condition is the expression x^3+y^3+z^3 factorable? Where x,y,z are positive whole numbers.
  2. jcsd
  3. Feb 25, 2013 #2


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    well it seems to factor if x=1, y=2, z=3, and if x=y=z ≥ 2, and more generally if gcd(x,y,z) > 1.
  4. Feb 27, 2013 #3
    My bad for not stating before. Let's assume the gcd(x,y,z) =1 and gcd(x,y)>1
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