# Floor Function Multiplied By Fractional Part

Algebra Level 4

Find the number of solutions for the equation $$\{ x\} \lfloor x \rfloor = x$$ for $$x \in [-100,100]$$.

Details and assumptions:

$$\{ x\}$$ denotes the fractional part of $$x$$. $$\lfloor x \rfloor$$ denotes the greatest integer lesser than or equal to $$x$$.

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