scholarly journals On the complexity of algebraic numbers, II. Continued fractions

2005 ◽  
Vol 195 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Boris Adamczewski ◽  
Yann Bugeaud
Keyword(s):  
Continued Fractions ◽  
Algebraic Numbers

Continued Fractions of Algebraic Numbers

1995 ◽  
pp. 137-152 ◽  
Author(s):  
Enrico Bombieri ◽  
Alfred J. van der Poorten
Keyword(s):  
Continued Fractions ◽  
Algebraic Numbers

Fibonacci numbers in generalized Pell sequences

2020 ◽  
Vol 70 (5) ◽  
pp. 1057-1068
Author(s):  
Jhon J. Bravo ◽  
Jose L. Herrera
Keyword(s):  
Lower Bounds ◽  
Continued Fractions ◽  
Fibonacci Numbers ◽  
Independent Interest ◽  
Linear Forms In Logarithms ◽  
Algebraic Numbers ◽  
Linear Forms ◽  
Pell Numbers

AbstractIn this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for Fibonacci numbers in the Pell sequence.

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