An algebra problem by Vishwesh Kumar

Consider the 2 functions: $f\left( x \right) =x^{ 3 }+ax^{ 2 }+bx+c\\ g\left( x \right) =x^{ 3 }+bx^{ 2 }+cx+a$

Given:

(i) f(1)=0

(ii) roots of g(x) are squares of roots of f(x)

Find $a^{ 2013 }+b^{ 2013 }+c^{ 2013 }$

This question was asked in Regional Mathematics Olympiads 2013 of class 10th