Solving the Pell equation via Rédei rational functions

Details Solving the Pell equation via Rédei rational functions Solving the Pell equation via Rédei rational functions

2011-03-19

arxiv.org/abs/1103.3762v1

The Fibonacci Quarterly, Vol. 48, p. 348-357, 2010

Mathematics

Number Theory

11 pages

Scientific paper

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.

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