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Let f(x)=x3+ax2+bx+c f(x) = x^3 + ax^2 + bx + cf(x)=x3+ax2+bx+c and g(x)=x3+bx2+cx+a g(x) = x^3 + bx^2 + cx + ag(x)=x3+bx2+cx+a, where a,b,ca, b, ca,b,c are integers with c≠0c\not = 0c=0. Suppose the following conditions hold :
f(1)=0f(1)= 0f(1)=0.
The roots of g(x)g(x)g(x) are squares of roots of f(x)f(x)f(x).
Find the value of a2013+b2013+c2013a^{2013}+b^{2013}+c^{2013}a2013+b2013+c2013.
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