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Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a, where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0, (b) 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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