Geodesic
Rational Points in $m$-adic Cantor Sets
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 2, pp. 9-14

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

For any natural numbers $m\geq 3$ and $s$, $0$ it is defined Cantor $m$-adic sets $C(m,s)$, the set of real numbers in segment [0, 1] having an expansion on base $m$ without the cipher $s$. It is proved that for any prime number $p>m^2$ the set of simplified fractions of the form $\tfrac{s}{p^t}$ where $s$ and $t$ are and integer is finite (possibly empty).
Keywords: Cantor perfect set, $m$-adic expansion.
Mots-clés : rational point 
@article{VNGU_2014_14_2_a1,
     author = {V. Bloshchitsyn},
     title = {Rational {Points} in $m$-adic {Cantor} {Sets}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {9--14},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a1/}
}
TY  - JOUR
AU  - V. Bloshchitsyn
TI  - Rational Points in $m$-adic Cantor Sets
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2014
SP  - 9
EP  - 14
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a1/
LA  - ru
ID  - VNGU_2014_14_2_a1
ER  - 
%0 Journal Article
%A V. Bloshchitsyn
%T Rational Points in $m$-adic Cantor Sets
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2014
%P 9-14
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a1/
%G ru
%F VNGU_2014_14_2_a1
V. Bloshchitsyn. Rational Points in $m$-adic Cantor Sets. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 2, pp. 9-14. http://geodesic.mathdoc.fr/item/VNGU_2014_14_2_a1/