Find ALL integer solutions of
x*y*z=x+y+z.

Same question if non-integer solutions are accepted.

A little algebra shows that x=(y+z)/(yz-1).  The equation can be satisfied for any choice of y and z, as long as their product is not 1. 

By inspection, one set of integer solutions are in the form {0,-n,n} for any integer n.

Posted by Bryan on 2013-04-04 10:20:44