# What's the concept ??

Algebra Level 4

Let $$f(x)$$ be an invertible function and $$g(x)$$ be its inverse function . It is given that $$f(x)=x$$ for only one value of $$x$$ in the range of $$g(x).$$

What is the number of values of $$x$$ in the domain of $$f(x)$$ for which $$f(x)-g(x)=n-\lfloor \frac{2015}{4} \rfloor$$ ? ,where $$n$$ is the only natural number for which the polynomial $$1+x+x^2+x^3+...+x^{n-1}$$ divides the polynomial $$1+x^2+x^4+...+x^{2010}.$$

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