An algebra problem by Mehul Chaturvedi

Algebra Level 4

Let f(x)=x3+ax2+bx+cf(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 c0.c\neq0. Suppose that the following conditions hold:

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

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

Find the value of a2013+b2013+c2013.a^{2013}+b^{2013}+c^{2013}.

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