Function No. 2013
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 \(c\not = 0\). Suppose the following conditions hold :
\(f(1)= 0\).
The roots of \(g(x)\) are squares of roots of \(f(x)\).
Find the value of \(a^{2013}+b^{2013}+c^{2013}\).
by
Anish Harsha