In this paper, we define a new product over R U {\infty}, which allows us to obtain a group isomorphic to R* with the usual product. This operation unexpectedly offers an interpretation of the Rédei 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.

### Solving the Pell equation via Rédei rational functions

#### Abstract

In this paper, we define a new product over R U {\infty}, which allows us to obtain a group isomorphic to R* with the usual product. This operation unexpectedly offers an interpretation of the Rédei 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.
##### Scheda breve Scheda completa Scheda completa (DC)
48
348
357
http://arxiv.org/pdf/1103.3762.pdf
http://www.fq.math.ca/48-4.html
continued fractions; groups over conics; Pell hyperbola; Pell equation; Rédei rational functions
Stefano Barbero; Umberto Cerruti; Nadir Murru
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/75599