I would try it in python:
for i in range(43):
  for j in range(i,43-i):
    for k in range(j,43-j):
      if i+j+k==43 and i**3+j**3+k**3==17299:
        print i,j, k

however, it's NOT the square of 17299, but simply 17299 (if you check for
the square, you get no solution)

Axel


On Sat, Jul 16, 2011 at 11:54 AM, micke <[email protected]> wrote:

> What are the three positive integers whose sum is 43. and the sum of
> the cubes of three integers is square of the number 17299.
>
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