# Removing Floors

Algebra Level 3

$\large \left \lfloor \dfrac n2 \right \rfloor + \left \lfloor \dfrac n3 \right \rfloor + \left \lfloor \dfrac n5 \right \rfloor = \dfrac n2 + \dfrac n3 + \dfrac n5$

If $n$ is a natural number and $1\leqslant n \leqslant 100$, then find the number of solutions to the equation above.

Notation: $\lfloor \cdot \rfloor$ denotes the floor function.

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