Displaying similar documents to “Metric and arithmetic properties of mediant-Rosen maps”

Arithmetic diophantine approximation for continued fractions-like maps on the interval

Avraham Bourla (2014)

Acta Arithmetica

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We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.

On the diophantine equation x²+x+1 = yz

A. Schinzel (2015)

Colloquium Mathematicae

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All solutions of the equation x²+x+1 = yz in non-negative integers x,y,z are given in terms of an arithmetic continued fraction.

An extension of a theorem of Duffin and Schaeffer in Diophantine approximation

Faustin Adiceam (2014)

Acta Arithmetica

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Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.