# Drop it Like it's a Floor Function

Algebra Level 5

Let $$n$$ be a positive real. If the number of real solutions to $nx^2=n\lfloor x^2\rfloor+x$ is $$2014$$, then the range of possible values of $$n$$ is $n\in (a,b\,]$ If $$b-a=N$$, then find the value of $\lfloor 1000N\rfloor$

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