Function No. 2013

Algebra Level 4

Let f(x)=x3+ax2+bx+c f(x) = x^3 + ax^2 + bx + c and g(x)=x3+bx2+cx+a g(x) = x^3 + bx^2 + cx + a, where a,b,ca, b, c are integers with c0c\not = 0. Suppose the following conditions hold :

  • f(1)=0f(1)= 0.

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

Find the value of a2013+b2013+c2013a^{2013}+b^{2013}+c^{2013}.

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