Preuve simplifiée du théorème de Serret sur les nombres équivalents

Abstract

If the continued fractions of two irrational numbers have a common complete quotient, then these two numbers are in the same orbit under the action of $\mathrm{PGL}(2,\mathbb{Z})$. The converse is Serret's well-known theorem, but we give a simpler and purely algebraic proof of it.

in French