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Solving the Pell equation via R\'edei rational functions

Abstract

In this paper, we define a new product over $\mathbb{R}^{\infty}$, which allows us to obtain a group isomorphic to $\mathbb R^*$ with the usual product. This operation unexpectedly offers an interpretation of the R\'edei rational functions, making more clear some of their properties, and leads to another product, which generates a group structure over the Pell hyperbola. Finally, we join together these results, in order to evaluate solutions of Pell equation in an original way.Comment: 11 page

Topics: Mathematics - Number Theory, 11A55, 11B39, 11D09
Year: 2011
OAI identifier: oai:arXiv.org:1103.3762