Geodesic
On the sequence of fractional parts of the ratio of Fibonacci numbers $x_{n+1}=\left\{\frac{F_{n+1}}{F_n}x_n\right\}$
Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 242-250

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In this paper for the expension of real numbers on Fibonacci sequence theorems on the uniform distribution of remainders for almost of all real numbers in the sense of Lebesgue's measure. the conclusion of this theorem is based on the Weyl's criteria of the uniform distribution of a sequence modulo unit and on the lemma.
Keywords: the Fibonacci's sequence, H.Weyl's criteria, lemma of Borel – Kantelli. 
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     author = {A. Kh. Ghiyasi and I. P. Mikhailov and V. N. Chubarikov},
     title = {On the sequence of fractional parts of the ratio of {Fibonacci} numbers $x_{n+1}=\left\{\frac{F_{n+1}}{F_n}x_n\right\}$},
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A. Kh. Ghiyasi; I. P. Mikhailov; V. N. Chubarikov. On the sequence of fractional parts of the ratio of Fibonacci numbers $x_{n+1}=\left\{\frac{F_{n+1}}{F_n}x_n\right\}$. Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 242-250. http://geodesic.mathdoc.fr/item/CHEB_2023_24_3_a12/