2016 is absolutely awesome 15

Algebra Level 4

Let f(x)=x3+ax2+bx+cf(x) = x^3 + ax^2 + bx + c and g(x)=x3+bx2+cx+ag(x) = x^3 + bx^2 + cx + a, where a,b,ca, b, c are integers with c0c \ne 0.

Suppose that the following conditions hold:

  • f(1)=0f(1) = 0

  • the roots of g(x)g(x) are squares of the roots of f(x)f(x).

Find the value of S=a2016+b2016+c2016S=a^{2016}+b^{2016}+ c^{2016}.


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