Displaying similar documents to “A function from Diophantine approximations.”

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.

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.