Geodesic
Representations of positive integers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 57-59 
V. G. Chirskii; V. Yu. Matveev. Representations of positive integers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 57-59. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a11/
@article{VMUMM_2013_6_a11,
     author = {V. G. Chirskii and V. Yu. Matveev},
     title = {Representations of positive integers},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {57--59},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a11/}
}
TY  - JOUR
AU  - V. G. Chirskii
AU  - V. Yu. Matveev
TI  - Representations of positive integers
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2013
SP  - 57
EP  - 59
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a11/
LA  - ru
ID  - VMUMM_2013_6_a11
ER  - 
%0 Journal Article
%A V. G. Chirskii
%A V. Yu. Matveev
%T Representations of positive integers
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2013
%P 57-59
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a11/
%G ru
%F VMUMM_2013_6_a11

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

The problem of representing integers as sums of terms of a certain type is actual in number theory and its applications. We are interested in the average length of these expansions and the required number of auxiliary calculations. The paper deals with DBNS, chains and the polyadic (factorial) expansions of positive integers.

[1] Postnikov A.G., Vvedenie v analiticheskuyu teoriyu chisel, Nauka, M., 1971 | MR

[2] Dimitrov V.S., Jullien G.A., Miller W.C., “An algorithm for modular exponentiation”, Inform. Process. Lett., 66:3 (1998), 155–159 | DOI | MR

[3] Dimitrov V.S., Rowe E.W., “Lower bounds on the lenghts of double base representations”, Proc. Amer. Math. Soc., 159:10 (2011), 3423–3430 | DOI | MR

[4] Doche Ch., Imbert L., “Extended double-base number system with application to elliptic curve cryptography”, Proc. Conf. INDOCRYPT 2006, Springer-Verlag, Berlin–Heidelberg, 2006, 335–348 | DOI | MR

[5] Burger E.B., Clyde D.C., Colbert C.H., Gea Hyun Shin, Zhaoning Wang, “A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers”, Acta Arithmetica, 153:3 (2012), 217–249 | DOI | MR

[6] Chirskii V.G., Shakirov R.F., “O predstavlenii naturalnykh chisel s ispolzovaniem neskolkikh osnovanii”, Chebyshevskii sb., 2013, no. 1