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

CERRUTI, Umberto;MURRU, NADIR
2010-01-01

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.
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
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