# 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 $$1\leq x \leq n$$.


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

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