Abstract
A direct combinatorial proof is given to a generalization of the fact that the largest modulusN of a disjoint covering system appears at leastp times in the system, wherep is the smallest prime dividingN. The method is based on geometric properties of lattice parallelotopes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. A. Berger, A. Felzenbaum andA. S. Fraenkel, New results for covering systems of residue sets,Bull. Amer. Math. Soc. 14 (1986), 121–125.
P. Erdős, On a problem concerning systems of congruences (Hungarian; English summary),Mat. Lapok. 3 (1952), 122–128.
M. Newman, Roots of unity and covering sets,Math. Ann. 191 (1971), 279–282.
Š. Porubský,Results and Problems on Covering Systems of Residue Classes, Mitteilungen aus dem Math. Sem. Giessen, Heft 150, Universität Giessen, 1981.
Š. Znám, On exactly covering systems of arithmetic sequences,Number Theory, Colloq. Math. Societatis János Bolyai2 (P. Turán, ed.), Debrecen 1968, North-Holland, Amsterdam 1970, 221–225.
Author information
Authors and Affiliations
Additional information
This research was supported by grant 85-00368 from the United States-Is rael Binational Science Foundation, Jerusalem, Israel.
Rights and permissions
About this article
Cite this article
Berger, M.A., Felzenbaum, A. & Fraenkel, A.S. A non-analytic proof of the newman—znám result for disjoint covering systems. Combinatorica 6, 235–243 (1986). https://doi.org/10.1007/BF02579384
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02579384