Geodesic
Rational Points in $m$-adic Cantor Sets
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 2, pp. 9-14 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2014},
     volume = {14},
     number = {2},
     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
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
%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/

[1] Edgar G. A., Measure Topology and Fractal Geometry, Springer–Verlag, N.Y., 1990 | MR | Zbl

[2] Wall Ch. R., “Terminating Decimals in Cantor Ternary Set”, Fibonacci Quaterly, 28:2 (1990), 98–101 | MR | Zbl

[3] Nagy J., “Rational Points in Cantor Sets”, Fibonacci Quaterly, 39:3 (2001), 238–241 | MR | Zbl

[4] Boes D., Darst R., Erdös P., “Fat, Symmetry. Irrational Cantor Sets”, Amer. Math. Monthly, 88:5 (1980), 340–341 | DOI | MR

[5] I. M. Vinogradov, Background of the Number Theory, Nauka, M., 1981 (in Russian) | MR