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 $a^{2013}+b^{2013}+c^{2013}$ .