# A year problem by Nihar

Algebra Level 3

$\large \left(\dfrac{x(x+1)}{2}\right)^2 - \left(\dfrac{x(x-1)}{2}\right)^2=\dfrac{x^2}{n}$

Let $$S_{n}$$ be the sum of all values of $$x$$ that satisfy the above equation where $$n \ne 0$$.

If $$S_{2014}$$ can be expressed as $$\dfrac{a}{b}$$ where $$a,b$$are coprime integers, then what is the value of $$a+b$$?

Bonus: generalize this for all $$n$$.

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