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Un arbre de constantes d'approximation analogue à celui de l'équation diophantienne de Markoff

Serge Perrine (1998)

Journal de théorie des nombres de Bordeaux

La théorie de Markoff classique, construite autour de l’équation diophantienne x 2 + y 2 + z 2 = 3 x y z donne les constantes d’approximation des nombres irrationnels supérieures à ( 1 / 3 ) . Dans le présent article, on explicite une théorie équivalente autour de la valeur ( 1 / 4 ) . Elle est intimement liée à l’équation diophantienne x 2 + y 2 + z 2 = 4 x y z - x pour laquelle on construit explicitement un arbre associé.

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