  This paper deals with quadratic irrationals of the form $m/q+\sqrt v$ for
fixed positive integers $v$ and $q$, $v$ not a square, and varying integers
$m$, $(m,q)=1$. Two numbers $m/q+\sqrt v$, $n/q+\sqrt v$ of this kind are
equivalent (in a classical sense) if their continued fraction expansions can be
written with the same period. We give a necessary and sufficient condition for
the equivalence in terms of solutions of Pell's equation. Moreover, we
determine the number of equivalence classes to which these quadratic
irrationals belong.
