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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