方程组x^3+y^3+z^3=x+y+z且x^2+y^2+z^2=xyz是否存在整数解

manthanein

\(x^3+y^3+z^3=x+y+z\)
\(x^2+y^2+z^2=3xyz\)

考虑到：
\(x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)=\D \frac{(x+y+z)[(x-y)^2+(y-z)^2+(x-z)^2]}{2}\)