Hi!

I have a math problem:

we know $\displaystyle gcd(x;y;z)=1$,$\displaystyle x \neq y \neq z$ and $\displaystyle x,y,z>1$.

$\displaystyle gcd(\frac{(x+y)(y+z)(z+x)-(x-y)(y-z)(z-x)}{2}-xyz;$

$\displaystyle \frac{(x+y)(y+z)(z+x)+(x-y)(y-z)(z-x)}{2}-xyz;x+y+z)$

may have value?