Let x,y,z be positive integers such that HCF (x,y,z) = 1 and x² + y² = 2z² . Which of the following statements are true?

I.  4 divides x or 4 divides y.

II.  3 divides x + y or 3 divides x – y.

III.  5 divides z(x² – y²)

(A)  I and II only

(B)  II and III only

(C)  II only

(D)  III only