Solving the Pell equation via Rédei rational functions

Abstract

In this paper, we define a new product over ${\mathbb{R}}^{\infty }$, which allows us to obtain a group isomorphic to ${\mathbb{R}}^{\ast }$ 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.

11 pages