# Inspired by Calvin Lin - Part II

Algebra Level 5

$f(n)=x^2 + ( x -1) ^2 +(x+2)^2+\ldots+(x-2n+1)^2+(x+2n)^2$

As $$x$$ ranges over all real values, If the minimum value of $$f(n)$$ is $$\dfrac{3936170}{59}$$ for some natural number $$n$$, find the value of $$n$$.

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