I'm in this thread showed how do the solutions of this equation.
http://math.stackexchange.com/questions/885181/how-to-prove-c-b-2-3cb-x3-has-no-nonzero-integer-solutions/885372#885372https://math.stackexchange.com/questions/885181/how-to-prove-c-b-2-3cb-x3-has-no-nonzero-integer-solutions/885372#885372
Mutually simple solutions for one of these formulas are coming out.
$$x^2+xy+y^2=z^3$$
$$x=s^3+3ps^2-p^3$$
$$y=p^3+3p^2s-s^3$$
$$z=p^2+ps+s^2$$
If $p=2$ ; $s=3$ We get: $x=73$ ; $y=17$ ; $z=19$
The above example is not correct.
These decisions are determined by a formula.
$$x=s(p^2+ps+s^2)$$
$$y=p(p^2+ps+s^2)$$
$$z=p^2+ps+s^2$$
If $p=19$ ; $s=-18$ ; Then the solutions are. $x=-18(7^3)$ ; $y=19(7^3)$ ; $z=7^3$
That is equivalent to the solution. $x=-18$ ; $y=19$ ; $z=7$
