Which of the following conditions is sufficient to guarantee that integers x, y, and z satisfy the equation
x(x−y)+y(y−z)+z(z−x)=1?<spanclass=′latex−bold′>(A)</span>x>y and y=z<spanclass=′latex−bold′>(B)</span>x=y−1 and y=z−1<spanclass=′latex−bold′>(C)</span>x=z+1 and y=x+1<spanclass=′latex−bold′>(D)</span>x=z and y−1=x<spanclass=′latex−bold′>(E)</span>x+y+z=1