# Floors + Ceilings = Fun

Algebra Level 5

$\large \left\lfloor { x }^{ 2 }-1 \right\rfloor +\left\lceil { x }^{ 2 }-4 \right\rceil +\{ { x }^{ 3 }+1\} ={ x }^{ 2 }$

find the number of solutions to the above equation.

Notation: $$\{\cdot \}$$ denotes the fractional part function.

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