\(x,y,z\) are integers such that \( (x-y)^2+(y-z)^2+(z-x)^2=xyz\).

Prove that \(x^3+y^3+z^3\) is divisible by \(x+y+z+6\).

Prove that \(x^3+y^3+z^3\) is divisible by \(x+y+z+6\).

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TopNewest\(x^{3}+y^{3}+z^{3}-3xyz=1/2×(x+y+z)((x-y)^{2}+(y-z)^{2}+(z-x)^{2})\) Using this you can solve in 1 minute – Prince Loomba · 1 week, 3 days ago

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