English

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

Number Theory 2017-06-20 v1

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 PGL(2,Z)\mathrm{PGL}(2,\mathbb{Z}). The converse is Serret's well-known theorem, but we give a simpler and purely algebraic proof of it.

Keywords

Cite

@article{arxiv.1706.06082,
  title  = {Preuve simplifi\'ee du th\'eor\`eme de Serret sur les nombres \'equivalents},
  author = {Anne Bauval},
  journal= {arXiv preprint arXiv:1706.06082},
  year   = {2017}
}

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