# Newton's Sums with pi?

Algebra Level 5

$x+y+z=1\\ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }=\pi\\ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ \pi }^{ 2 }+3{ z }^{ 2 }-3z+1\\$

This set of equations is true for three complex numbers $$x, y, z$$.

If $$xyz-xy=\frac { A }{ B } {\pi }^{ C }$$ for positive integers $$A, B, C$$ and $$\gcd(A,B)=1$$, then find $$A+B+C$$.

First do this.

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