Then z=x+1/x-1; x can be 1, when z= (1+1-1)=1, which is a square, or x can be -1, when z=-1+-1-1 = -3, which is not a square.
It's always worth checking the proposition, before embarking on a proof!
(Incidentally, if y=2, x can take the value -4, when z is -5, while if y=-2, x can take the value -4, when z is -3.)
The answer might be different if x,y,z were required to be positive integers...
Edited on October 11, 2015, 1:52 pm
Posted by broll
on 2015-10-11 13:42:14