Let $x,y,z$ be positive integers such that:

$\frac{1}{x}- \frac{1}{y} = \frac{1}{z}$

If $h$ is the greatest common divisor of $x,y,z$ ,

then $hxyz$ and $h(y-x)$ are not perfect squares.

Is this statement true or false?

False
True

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Hint- we can write difference of any two numbers as a multiple of their HCF. Therefore, y-x=kh for some integer k And khxyz=(xy)^2 So, hxyz=(xy)^2/k but since I can be any integer not necessarily a square no. Therefore hxyz could not be perfect square all time.