# Function No. 2013

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 $$c\not = 0$$. Suppose the following conditions hold :

• $$f(1)= 0$$.

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

Find the value of $$a^{2013}+b^{2013}+c^{2013}$$.

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