let $x,y,z,n$ is positive integer,and such $$n=x^3+y^3+z^3-3xyz,n\le 2014$$
Find all the $n$ value
My idea: since $$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)$$
then I can't Thank you
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Again, $$x^2+y^2+z^2-xy-yz-xz=(x+y+z)^2-3(xy+yz+zx)$$ So, if we choose $x+y+z$ as integer factor of $n,$ we can immediately find $xy+yz+zx$ – lab bhattacharjee Mar 23 '14 at 04:31
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See the more general http://math.stackexchange.com/questions/724990/integers-can-be-expressed-as-a3b3c3-3abc for a solution. – user2345215 Mar 24 '14 at 21:13