Geodesic
On two relations characterizing the golden ratio
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 194-202

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V. G. Zhuravlev found two relations associated with the golden ratio: $\tau=\frac{1+\sqrt{5}}{2}$: $[([i\tau]+1)\tau]=[i\tau^2]+1$ and $[[i\tau]\tau]+1=[i\tau^2]$. We give a new elementary proof of these relations and show that they give a characterization of the golden ratio. Further we consider satisfability of our relations for finite sets of $i$-s and establish some forcing property for this situation. 
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     author = {A. A. Zhukova and A. V. Shutov},
     title = {On two relations characterizing the golden ratio},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a5/}
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A. A. Zhukova; A. V. Shutov. On two relations characterizing the golden ratio. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 194-202. http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a5/