Geodesic
On representations of positive integers
Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 75-85 
V. G. Chirskii; V. Y. Matveev. On representations of positive integers. Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of representing integers as sums of terms of s 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] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1984 | MR

[3] Novoselov E. V., “Topologicheskaya teoriya delimosti tselykh chisel”, Uchen. zap. Elabuzh. gos. ped. in-ta, 1960, no. 3, 3–23

[4] Chirskii V. G., Shakirov R. F., “O predstavlenii naturalnykh chisel s ispolzovaniem neskolkikh osnovanii”, Chebyshevskii sbornik, 14:1(45) (2013), 86–93

[5] Dimitrov V. S., Jullien G. A., Miller W. C., “An Algorithm for Modular Exponentiation”, Inform. Process. Lett., 66:3 (1998), 155–159 | DOI | MR | Zbl

[6] Dimitrov V. S., Rowe E. W., “Lower bounds on the lenghts of double base representations”, Proc. Amer. Math. Soc., 139:10 (2011), 3423–3430 | DOI | MR | Zbl

[7] Doche Ch., Imbert L., “Extended Double-Base Number System with Application to Elliptic Curve Cryptography”, INDOCRYPT 2006, LNCS, 4329, Springer-Verlag, 2006, 335–348 | MR | Zbl

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