Problem #4




Find six distinct positive integers A, B, C, X, Y, and Z such that



  1. A + B + C = X + Y + Z
  2. A^2 + B^2 + C^2 = X^2 + Y^2 + Z^2
  3. A^3 + B^3 + C^3 = X^3 + Y^3 + Z^3


[Compare with the last three problems.]





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