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Suppose we had an inequality $ax < by < cx$ where $a,b,c,x,y \in \mathbb Z$. If we fix $a,b,c$ and let $x,y$ vary how can we find the values of $x$ for which only a single $y$ satisfies the inequality. The only way I've managed to do this in to basically list the solutions and manually count the ones which satisfy the condition which is clearly impractical, especially for large values. Is there an easier way to do this?

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    No, not necessarily.2011-04-12

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