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

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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. 
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     author = {I. D. Kan},
     title = {Reachability of inequalities from {Lame's} theorem},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     url = {http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a4/}
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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/