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arXiv · 1706.06082

Preuve simplifi\'ee du th\'eor\`eme de Serret sur les nombres \'equivalents

Anne Bauval
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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.

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Anne Bauval. 2017-06-19. Preuve simplifi\'ee du th\'eor\`eme de Serret sur les nombres \'equivalents. https://arxiv.org/abs/1706.06082

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