If $q\ne0$, divide the cubic equation by $q^3$ and define the <rational numbers>
$$
\widetilde y=\frac yq,
\qquad
\widetilde x=\frac xq.
$$
Then every integer anomaly-free assignment supplies a rational solution of
$$
\boxed{54+18\widetilde y^{,2}+\widetilde x^{,3}=0,
\qquad \widetilde x,\widetilde y\in\mathbb Q}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 305 / 3 / iv / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-305/3/iv/solution