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How would you determine all integers $m$ such that the following is true?

$$\frac{1}{m}=\frac{1}{\lfloor 2x \rfloor}+\frac{1}{\lfloor 5x \rfloor} .$$

Note that $\lfloor \cdot \rfloor$ means the greatest integer function. Also, $x$ must be a positive real number.

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    Do you want to find all $m$ such that the equation is satisfied for *some* $x > 0$? (The question is missing the quantifier over $x$.)2011-10-30

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