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

Table of contents
- Solution iv

Solution

If

q \neq = 0

, divide the cubic equation by

q^{3}

and define the rational numbers

y = \frac{y}{q}, x = \frac{x}{q} .

Then every integer anomaly-free assignment supplies a rational solution of

54 + 18 y^{, 2} + x^{, 3} = 0, x, y \in Q .

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