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In this paper we study a general class of conics starting from a quotientfield. We give a group structure over these conics generalizing theconstruction of a group over the Pell hyperbola. Furthermore, we generalize thedefinition of R\'edei rational functions in order to use them for evaluatingpowers of points over these conics. Finally, we study rational approximationsof irrational numbers over conics, obtaining a new result for the approximationof quadratic irrationalities.

Generalized R\'edei rational functions and rational approximations over conics