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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## **closed** as off-topic by Michael Albanese, Greg Martin, Gerry Myerson, Andreas Blass, Steven Landsburg Feb 4 '18 at 23:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

- "This question does not appear to be about research level mathematics within the scope defined in the help center." – Michael Albanese, Greg Martin, Gerry Myerson, Andreas Blass, Steven Landsburg

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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 $x=-1,\; y=2,\; z=1$.