Partial fraction challenge (2)

Algebra Level 4

S=114+12+1+224+22+1+334+32+1++201620164+20162+1 S =\frac{1}{1^{4}+1^{2}+1}+\frac{2}{2^{4}+2^{2}+1}+\frac{3}{3^{4}+3^{2}+1}+\dots+\frac{2016}{2016^{4}+2016^{2}+1}

If the sum above S=2017p2017q+1S = \dfrac{2017p}{2017q+1}, where pp and qq are positive integers, find p+qp+q.

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