# An equation of fractional parts

Find the sum of all positive integers $$n$$ such that for some positive integer $$m\geq n$$, the following inequality is satisfied for all real $$x$$: $\left\{ \frac{x}{15} \right\}- \left\{ \frac{x}{n} \right\}-\left\{ \frac{x}{m} \right\} \leq 0.$

Details and assumptions

The function $$\{a\}$$ denotes the fractional part of $$a$$. It can be calculated as $$\{ a\} =a-\lfloor a \rfloor$$. As an explicit example, $$\{5\}=0$$, $$\{3.75\}=0.75$$, $$\{-4.2\}=0.8$$ .

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