Necessary conditions for distinct covering systems with square-free moduli

@inproceedings{Simpson1991NecessaryCF,
  title={Necessary conditions for distinct covering systems with square-free moduli},
  author={R. Jamie Simpson and Doron Zeilberger},
  year={1991}
}
is such a system. Guy (Section F13 of [5]) gives many fascinating problems on DCS's. For instance, does a DCS exist with all moduli odd? In this paper we shall be mainly concerned with DCS's whose moduli are square free. Such DCS's exist (see [5], p. 140) but none are known to exist with moduli odd and square free. This is in spite of Erdos's conjecture [4] that for every t there is a distinct covering system in which all moduli are square-free integers all of whose prime factors are greater… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-5 of 5 references

Fe lzen b a um, and Aviezri S. Fr a e n kel, Necessar)l eondit~on for the existence of an incongruent covering system with odd moduli

Marc A. Berger, Alexander
Acta Arith. 45(1985), • 1985

Slm p s o n , Regular coverings OJ the integers by arithmetic progressions

R J.
Acta Arith • 1985

K r u k e n be rg

C E.
Ph.D. thesis, Univ. of Illinois, • 1971

C h u r c h h o u s e, Coverzng sets and systems oj congruences, in Computers in Mathemat~cul Research (R

R F.
F . C h u r c h h o u s e and J. C. H e r t z , eds.), • 1968

Similar Papers

Loading similar papers…