Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-13T23:55:40.755Z Has data issue: false hasContentIssue false
  • English
  • Français

Covering systems of congruences, a negative result

Published online by Cambridge University Press:  26 February 2010

J. A. Haight
J. A. Haight
Affiliation:
Department of Mathematics, University College, London.

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Suppose that we have a system of congruences ai (mod ni) 1 < n1 < … < ni < … < nk such that every integer is congruent to at least one ai (mod ni), then we say that it is a covering system of congruences. If ni | m, 1 ≤ i ≤ k, we say that m is a covering number. We shall use the symbol ℕ to denote the natural numbers together with zero, then m is a covering number if, for each q there is an aq such that

Information

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 53 - 61
Copyright
Copyright © University College London 1979

References

1.Choi, S. L. G.. “Covering the set of integers by congruence classes of distinct moduli”, Math. Comp., 25 (1971). 885–895.CrossRefGoogle Scholar
2.Erdös, P.. “On integers of the form 2k + p and some related problems”, Summa Brasil Math., 11 (1950), 113–123.Google Scholar
3.Erdös, P.. “Problems in combinatorial number theory III” Lecture Notes in Mathematics, 626, Number Theory Day (Springer-Verlag), 43–72.Google Scholar
4.Schinzel, A.. “Reducibility of polynomials and covering systems of congruences”, Acta Arith., 13 (1967–68), 91–101.CrossRefGoogle Scholar