Of course, so the system to have a solution, we need x,y,z≥1.
Now squaring, we get : x2−y=z2−2z+1 and cyclically.
Summing up, we get : x+y+z=3, which implies x=y=z=1 as x,y,z≥1
Conversely, (1,1,1) is a solution to the system, so we're done.
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.