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.
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