  A Theorem of V.Ovsienko characterizes sequences of positive integers
$(a_1,a_2,\ldots,a_n)$ such that the $(2\times2)$-matrix $\begin{pmatrix} a_n &
-1 \\ 1 & 0 \end{pmatrix}\cdots \begin{pmatrix} a_1 & -1 \\ 1 & 0
\end{pmatrix}$ is equal to $\pm Id$. In this paper, we study this equation when
we replace $\pm Id$ by $\pm M$. In particular, we give a combinatorial
description of the solutions of this equation in terms of dissections of convex
polygons in the cases $M=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ and
$M=\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$.
