Show that none of the following numbers can have a purely periodic continued fraction:
$a-\sqrt b$, $a+\sqrt b$ with $a<0$, $a+\sqrt b$ with $b<1/4$
where $a,b\in \Bbb{Q}$ and $b>0$ s.t. $b$ is not a square of some rational numeber
I think I did the first one but I am not sure. Also, I have no idea with the other two. Could you please give me some hints?
*We have not taught "$a$ is purely periodic $\iff a$ is a reduced root"