Abstract
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.
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