9. Let $\left[a_{0} ; a_{1}, a_{2}, \ldots, a_{n}\right]$ be the simple continued fraction expansion of $r / s$ where $(r, s)=1$ and $r \geqslant 1$. Show that this continued fraction is symmetric, i.e. $a_{0}=a_{n}, a_{1}=a_{n-1}, a_{2}=a_{n-2}, \ldots$, if and only if $s \mid\left(r^{2}+1\right)$ if $n$ is odd and $s \mid\left(r^{2}-1\right)$ if $n$ is even. (Hint: Use problem 6 and Theorem 10.10).