Old and new necessary and sufficient conditions on ( a i , m i ) in order that n ≡ a i ( mod m i ) be a covering system

Štefan Porubský; Johanan Schönheim

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 4, page 341-349
  • ISSN: 0232-0525

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Porubský, Štefan, and Schönheim, Johanan. "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." Mathematica Slovaca 53.4 (2003): 341-349. <http://eudml.org/doc/32322>.

@article{Porubský2003,
author = {Porubský, Štefan, Schönheim, Johanan},
journal = {Mathematica Slovaca},
keywords = {arithmetic sequence; covering system; exactly covering system; disjoint covering system},
language = {eng},
number = {4},
pages = {341-349},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
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},
url = {http://eudml.org/doc/32322},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Porubský, Štefan
AU - Schönheim, Johanan
TI - 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
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 4
SP - 341
EP - 349
LA - eng
KW - arithmetic sequence; covering system; exactly covering system; disjoint covering system
UR - http://eudml.org/doc/32322
ER -

References

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  1. BEEBEE J., Bernoulli covers and exact covering systems, Amer. Math. Monthly 99 (1992), 946-948. (1992) MR1190561
  2. ERDÖS P.-GRAHAM R. L., Old and New Problems in Combinatorial Number Theory, Monographic No. 28 de L'Enseigment Mathematique, Universite Geneneve, 1980. (1980) MR0592420
  3. FRAENKEL A. S., A characterization of exactly covering congruences, Discrete Math. 4 (1973), 359-366. (1973) Zbl0257.10003MR0316359
  4. PORUBSKÝ Š., Covering systems and generating functions, Acta Arith. 26 (1975), 223-231. (1975) Zbl0268.10044MR0379423
  5. PORUBSKÝ Š., On m-times covering systems, Acta Arith. 29 (1976), 159-169. (1976) Zbl0282.10033MR0399033
  6. PORUBSKÝ Š., Identities involving covering systems I, Math. Slovaca 44 (1994), 153-162. (1994) Zbl0809.11012MR1282532
  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. (1999) MR1954716
  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). 
  9. SCHÖNHEIM J., Covering congruences related to modular arithmetic and error correcting codes, Ars Combin. 16-B (1983), 21-25. (1983) Zbl0535.10049MR0737106
  10. SUN Z.-W., Several results and systems of residue classes, Math. China 18 (1989), 251-252. (1989) 
  11. ZNÁM Š., A simple characterization of disjoint covering systems, Discrete Math. 12 (1975), 89-91. (1975) Zbl0306.10001MR0376597

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