> 
> Suppose $\gcd(a,b)=1$. Does this necessarily imply that $\gcd(a,2b)=1$? 
> 
> 
> 

If $\gcd(a,b)=1$ then $\exists x,y \in \Bbb{Z} (ax+by =1)$

I don't see how to manipulate this equation to give me $ax+2by \neq 1$ I'm assuming that's what I have to do?