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what is x+y+z is x,y and z are integers and xy-1 is divisible by z, yz-1 is divisible by x and xz-1 is divisible by y.

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It could be any integer: for $x+y+z=s \ne 2$, try $x=1,\;y=1,\;z=s-2$, or for $x+y+z=2$, try $x=-1,\; y=2,\; z=1$.

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