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# Prove this

$$x,y,z$$ 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 $$x+y+z+6$$.

Note by Abhishek Alva
7 months, 2 weeks ago

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$$x^{3}+y^{3}+z^{3}-3xyz=1/2×(x+y+z)((x-y)^{2}+(y-z)^{2}+(z-x)^{2})$$ Using this you can solve in 1 minute · 7 months, 2 weeks ago