G.I.F. Problem!

Algebra Level 5

Let \(n\geq 2\) be a positive integer. In terms of \(n\), find the number of roots of \(x^2 - \lfloor x^2 \rfloor = ( x- \lfloor x \rfloor )^2\) where \(1\leq x \leq n\).

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Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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