Geodesic
Reachability of inequalities from Lame's theorem
Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 45-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the following result is proved. The number of steps in Euclid's algorithm for two natural arguments, the smaller of which has $v$ digital digits in the decimal system, does not exceed the integer part of the fraction \linebreak $(v+ \lg ({\sqrt{5}}/ {\Phi}))/ \lg \Phi$, where $\Phi=(1+\sqrt{5})/2$, and this estimate is achieved for every natural $v$. It is also proved that partial or asymptotic reachability is valid for the other two known upper bounds on the length of the Euclid algorithm. 
@article{DVMG_2024_24_1_a4,
     author = {I. D. Kan},
     title = {Reachability of inequalities from {Lame's} theorem},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a4/}
}
TY  - JOUR
AU  - I. D. Kan
TI  - Reachability of inequalities from Lame's theorem
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2024
SP  - 45
EP  - 54
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a4/
LA  - ru
ID  - DVMG_2024_24_1_a4
ER  - 
%0 Journal Article
%A I. D. Kan
%T Reachability of inequalities from Lame's theorem
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2024
%P 45-54
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a4/
%G ru
%F DVMG_2024_24_1_a4
I. D. Kan. Reachability of inequalities from Lame's theorem. Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 45-54. http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a4/

[1] Nesterenko Yu. V., Teoriya chisel, Izdatelskii tsentr “Akademiya”, M., 2008

[2] Knut D. E., Iskusstvo programmirovaniya, v. 2, Izdatelstvo “Dialektika-Vilyams”, 1998 | MR

[3] Vorobev N. N., Chisla Fibonachchi, Glavnaya redaktsiya fiziko-matematicheskoi literatury izdatelstva “Nauka”, M., 1978

[4] Veil G., “O ravnomernom raspredelenii chisel po modulyu”, Izbrannye trudy, Nauka, M., 1984, 58–93