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 ?

**Answer Choices**

A. x>y and y=z

B. x=y-1 and y=z-1

C. x=z+1 and y=x+1

D. x=z and y-1=x

E. x+y+z=1

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 ?

**Answer Choices**

A. x>y and y=z

B. x=y-1 and y=z-1

C. x=z+1 and y=x+1

D. x=z and y-1=x

E. x+y+z=1