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For what values of $m$ do the equations $m x-1000=1001$ and $1001 x=m-1000 x$ have a common root?
The roots of these equations are the numbers $2001 / m$ and $m / 2001$ respectively. ${ }^{2001} / m=m / 2001 \Leftrightarrow m^{2}=2001^{2}$ $m= \pm 2001$

## Answer

For $m= \pm 2001$.

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