About statistics of periods of continued fractions of quadratic irrationalities

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+px=q with integer p and q, p ²+q ²≤R ². We prove a weak variant of Arnold conjectures about the Gauss–Kuzmin statistics with R→∞.