Generalized palindromic continued fractions
نویسندگان
چکیده
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...
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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...
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A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2018
ISSN: 0035-7596
DOI: 10.1216/rmj-2018-48-1-219