Say y=1.
Then z=x+1/x1; x can be 1, when z= (1+11)=1, which is a square, or x can be 1, when z=1+11 = 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 20151011 13:42:14 