1)If gcd(x,3)=1 and gcd(y,3)=1, prove that $\displaystyle x^2 + y^2$ cannot be a perfect square.

2)Given that gcd(a,b,c)lcm(a,b,c) = abc, prove that gcd(a,b)=gcd(b,c)=gcd(a,c)=1.

This is not homework, I'm doing it for extra practice, but I can't figure out how to prove these.

Any help would be appreciated!

[also under discussion in math link forum]