1, 2, 3, _ ?

Algebra Level 4

x,yx, y and zz are complex numbers satisfying

{x1+y1+z1=1x2+y2+z2=2x3+y3+z3=3 \begin{cases} x^1+y^1+z^1 & = 1\\ x^2 + y^2 + z^2 & = 2 \\ x^3 + y^3 + z^3 & = 3 \\ \end{cases}

The value of x4+y4+z4 x^4 + y^4 + z^4 can be expressed as ab \frac {a}{b} , where a a and bb are positive coprime integers. What is the value of a+b a +b ?

This problem is proposed by Harshit.

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