I need to present that each one the rational options of the equation $x^3+y^3+z^3=1$ may be given by giving rational values of $(s,t)$ on the formulation:
It’s straightforward to indicate that these formulation fulfill the equation, however I have not discovered a method to show the converse.
My thought was to jot down $s$ and $t$ as a quotient of polynomials in $x,y,z$, however I have not been ready to take action. I believe the denominator of those expressions shall be a second diploma polynomial in $z$, however I do not know the best way to proceed.
Any assist can be appreciated. Thanks upfront.
I’m conscious that this query has been requested earlier than on the positioning (see this), however the solutions given appear to be incorrect.