Guest wrote:For the given problem, how do we adapt the Newton Method to find integral solutions (assuming their existence) as fast as possible?

We should also consider what we know and what we seek:

We have an integral solution to equation,

1. [tex]a^{3}+b^{3}+c^{3}= 33[/tex].

We seek an integral solution to equation,

E. [tex]x^{3}+y^{3}+z^{3}= 42[/tex].

Moreover, we have an integral solution to equation,

2. [tex]e^{3}+f^{3}+g^{3}= 52[/tex].

So between the solutions of equations, one and two, we should be able find a solution to equation E if it exists...

Dave.