# Article

 Title: Old and new necessary and sufficient conditions on $(a_i, m_i)$ in order that $n\equiv a_i (\operatorname {mod} m_i)$ be a covering system (English) Author: Porubský, Štefan Author: Schönheim, Jochanan Language: English Journal: Mathematica Slovaca ISSN: 0139-9918 Volume: 53 Issue: 4 Year: 2003 Pages: 341-349 . Category: math . MSC: 11B25 idZBL: Zbl 1071.11012 idMR: MR2025467 . Date available: 2009-09-25T14:15:35Z Last updated: 2012-08-01 Stable URL: http://hdl.handle.net/10338.dmlcz/132814 . Reference: [1] BEEBEE J.: Bernoulli covers and exact covering systems.Amer. Math. Monthly 99 (1992), 946-948. MR 1190561 Reference: [2] ERDÖS P.-GRAHAM R. L.: Old and New Problems in Combinatorial Number Theory.Monographic No. 28 de L'Enseigment Mathematique, Universite Geneneve, 1980. MR 0592420 Reference: [3] FRAENKEL A. S.: A characterization of exactly covering congruences.Discrete Math. 4 (1973), 359-366. Zbl 0257.10003, MR 0316359 Reference: [4] PORUBSKÝ Š.: Covering systems and generating functions.Acta Arith. 26 (1975), 223-231. Zbl 0268.10044, MR 0379423 Reference: [5] PORUBSKÝ Š.: On m-times covering systems.Acta Arith. 29 (1976), 159-169. Zbl 0282.10033, MR 0399033 Reference: [6] PORUBSKÝ Š.: Identities involving covering systems I.Math. Slovaca 44 (1994), 153-162. Zbl 0809.11012, MR 1282532 Reference: [7] PORUBSKÝ Š.-SCHÖNHEIM J.: Covering systems of Paul Erdös: past, present and future.In: Proceeding of the International Conference Paul Erdös and his Mathematics Budapest 1999 (G. Halász, L. Lovász, M. Simonovits, V .T. Sós, eds.), Bolyai Soc. Math. Stud. 11, Springer Verlag/János Bolyai Math. Society, Berlin-Heidelberg-New York/Budapest, 2002, pp. 581-627. MR 1954716 Reference: [8] PORUBSKÝ Š.-SCHÖNHEIM J.: New necessary and sufficient conditions on $(a_i,m_i)$ in order that $x = a_i$ (mod m) be a covering system.Discrete Math. (To appear). Reference: [9] SCHÖNHEIM J.: Covering congruences related to modular arithmetic and error correcting codes.Ars Combin. 16-B (1983), 21-25. Zbl 0535.10049, MR 0737106 Reference: [10] SUN Z.-W.: Several results and systems of residue classes.Math. China 18 (1989), 251-252. Reference: [11] ZNÁM Š.: A simple characterization of disjoint covering systems.Discrete Math. 12 (1975), 89-91. Zbl 0306.10001, MR 0376597 .

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