Let $\mathrm{x}, \mathrm{y}, \mathrm{z}$ be positive integers such that $\mathrm{HCF}(\mathrm{x}, \mathrm{y}, \mathrm{z})=1$ and $\mathrm{x}^{2}+\mathrm{y}^{2}=2 \mathrm{z}^{2}$. Which of the following statements are true? I. 4 divides $\mathrm{x}$ or 4 divides $\mathrm{y}$. II. 3 divides $\mathrm{x}+\mathrm{y}$ or 3 divides $\mathrm{x}-\mathrm{y}$. III. 5 divides $z\left(x^{2}-y^{2}\right)$

• A

  I and II only
• Correct answer
  B

  II only
• C

  II and III only
• D

  III only

Hence, the correct answer is option: 'B'.