منابع مشابه
Palindromic continued fractions
An old problem adressed by Khintchin [15] deals with the behaviour of the continued fraction expansion of algebraic real numbers of degree at least three. In particular, it is asked whether such numbers have or not arbitrarily large partial quotients in their continued fraction expansion. Although almost nothing has been proved yet in this direction, some more general speculations are due to La...
متن کاملFactorization and Palindromic Continued Fractions
Abstract We provide elementary explanations in terms of palindromic continued fraction expansions for the factorization of integers of the form a2 + 1, including Fermat numbers and Cunningham project numbers. This provides a generalization and more complete explanation of the factorization of the sixth Fermat number given by Freeman Dyson at the turn of the century. This explanation may provide...
متن کاملGeneralized Continued Logarithms and Related Continued Fractions
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...
متن کاملContinued Logarithms and Associated Continued Fractions
We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such for...
متن کاملPeriodic Continued Fractions And
We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2007
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2306