1) If gcd(x,3)=1 and gcd(y,3)=1, prove that 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]