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arXiv · 1103.3762

Solving the Pell equation via Rédei rational functions

Stefano Barbero·Umberto Cerruti·Nadir Murru
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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 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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Stefano Barbero, Umberto Cerruti, Nadir Murru. 2011-03-19. Solving the Pell equation via Rédei rational functions. https://arxiv.org/abs/1103.3762

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