# 2016 is absolutely awesome 15

Algebra Level 4

Let $$f(x) = x^3 + ax^2 + bx + c$$ and $$g(x) = x^3 + bx^2 + cx + a$$, where $$a, b, c$$ are integers with $$c \ne 0$$.

Suppose that the following conditions hold:

• $$f(1) = 0$$

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

Find the value of $$S=a^{2016}+b^{2016}+ c^{2016}$$.

×