# An algebra problem by Mehul Chaturvedi

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 $$c\neq0.$$ Suppose that the following conditions hold:

(i) $$f(1)=0;$$

(ii) the roots of $$g(x)=0$$ are the squares of the roots of $$f(x)=0.$$

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

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