# For which I came here

Algebra Level 4

Let $$f(x) = x^3+ax^3+bx+c,g(x)=x^3+bx^2+cx+a$$ for integers $$a,b,c$$ with $$c\ne 0$$. Suppose the following conditions hold:

1. $$f(1)=0$$,

2. The roots of $$g(x)=0$$ are square of the roots of $$f(x) = 0$$.

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

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