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How can I show that two arbitrary rational numbers \begin{equation} x=\frac{a}{b} \ \ \text{and} \ \ y=\frac{c}{d} \end{equation} are linearly dependent over $\mathbb{Z}$.

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1 Answer 1

With $\alpha=bc$ and $\beta=-ad$ we have $$\alpha x+\beta y=0$$

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