Polynomial Remainder

Algebra Level 5

Consider the function f(x)=x2015+2015 f(x)=x^{2015}+2015 . If f(x) f(x) is divided by x8x6+x4x2+1 x^{8}-x^{6}+x^{4}-x^{2}+1 , it leaves a remainder g(x) g(x) . If f(x) f(x) is divided by (x+1)3 (x+1)^{3} , it has a remainder h(x) h(x).

Find the value of h(1)+11g(1) \frac{h(1)+1}{1-g(-1)}.

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