If $a$ and $b$ are relatively prime integers then prove that ($a$ ,$b^2$) =1 From the title I've stucked in this question for half an hour. Could anyone help me?

We have 
$$
(a,b)=1 \iff  ax+by=1 \text{   for  some integer $x,y$} 
$$
Then 
$$
(ax+by)^2=1 \implies a(ax^2+2bxy)+b^2 y^2=1 \implies (a,b^2)=1.
$$
