Of course, so the system to have a solution, we need $x,y,z \geq 1$. Now squaring, we get : $x^2 - y = z^2 - 2z + 1$ and cyclically. Summing up, we get : x+y+z=3, which implies x=y=z=1 as $x,y,z \geq 1$ Conversely, (1,1,1) is a solution to the system, so we're done.

hey , 4 ur answer u did not prove that (1,1,1) is the only solution so , ur answer is partially correct

liamthe3 wrote: hey , 4 ur answer u did not prove that (1,1,1) is the only solution so Yes they did. That's what the inequalities in the first three lines of the solution are for.