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?

If some integer $d$ divides $b$, then we can write $b = dx$ for some $x \in \mathbb{Z}$.  From this, we have $b^2 = (dx)^2 = d(dx^2)$, so $d$ also divides $b^2$.
Now look back to the definition for $\gcd$.  What if $d|a$ and $d|b^2$ wherein $d \neq 1$?
