  In this paper we answer certain questions posed by V.I. Arnold, namely, we
study periods of continued fractions for solutions of quadratic equations in
the form $x^2+p x=q$ with integer $p$ and $q$, $p^2+q^2\le R^2$. Our results
concern the average sum of period elements and Gauss--Kuzmin statistics as
$R\to\infty$.
