# Sum of 2 cubes ?

1. May 24, 2010

### cragar

1. The problem statement, all variables and given/known data
1729 is the smallest positive integer that can be represented in two different ways as the sum of two cubes , what are the two ways.
They have to be natural numbers.
3. The attempt at a solution

x^3+Y^3=1729 i could just find the answer by guess and check , but im not sure how to do it analytically.

2. May 24, 2010

### HallsofIvy

You can simplify a little by using $x^3+ y^3= (x+ y)(x^2- xy+ y^2)$.

Now, factor 1729 to find two factors that would fit that.

3. May 24, 2010

### cragar

sweet thanks for the help

4. May 25, 2010

### Mentallic

I remember my teacher showing us a method with complex numbers and moduli to find the sum of two squares to equal some number we have. If only I remember the method... Maybe this can be extended to the sum of two cubes?

5. May 26, 2010