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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