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Let x,y,z be positive integers such that...

Let x,y,z be positive integers such that HCF(x,y,z)=1 and `x^(2)+y^(2)=2z^(2)`. 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(x^(2-y^(2)))`

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