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x+y+z=0x2+y2+z2=ex3+y3+z3=e2x+y+z=0\\ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }=e\\ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ e }^{ 2 }\\ x+y+z=0x2+y2+z2=ex3+y3+z3=e2
This set of equations is true for three complex numbers x,y,zx, y, zx,y,z, where eee is Euler's Constant.
If xyz=ABeCxyz=\frac { A }{ B } { e }^{ C }xyz=BAeC for positive integers A,B,CA,B,CA,B,C with coprime A,BA,BA,B, find A+B+CA+B+CA+B+C.
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