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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