Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On infinite disjoint covering systems

Authors: Aviezri S. Fraenkel and R. Jamie Simpson
Journal: Proc. Amer. Math. Soc. 119 (1993), 5-9
MSC: Primary 11B25
MathSciNet review: 1148023
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The structure of all infinite incongruent disjoint covering systems (IIDCS) whose moduli are divisible by no prime $ > 3$ is given. It is then shown that this structure characterizes the subset of IIDCS for which the greatest common factor of all the moduli is $ 1$, and the set of primes dividing the moduli is finite.

References [Enhancements On Off] (What's this?)

  • [1] J. Beebee, Examples of infinite, incongruent exact covers, Amer. Math. Monthly 95 (1988), 121-123. MR 935423 (89g:11013)
  • [2] M. A. Berger, A. Felzenbaum, A. S. Fraenkel, and R. Holzman, On infinite and finite covering systems, Amer. Math. Monthly 98 (1991), 739-742. MR 1130685 (92g:11009)
  • [3] J. Dewar, On finite and infinite covering sets, Proc. Washington State Univ. Conf. on Number Theory (Washington State Univ., Pullman, WA) (J. H. Jordan and W. A. Webb, eds.), Washington State Univ. Press, Pullman, WA, 1971, pp. 201-206. MR 0318048 (47:6597)
  • [4] C. E. Krukenberg, Covering sets of the integers, Ph.D. Thesis, Univ. of Illinois, Urbana-Champaign, IL, 1971.
  • [5] R. J. Simpson and D. Zeilberger, Necessary conditions for distinct covering systems with square-free moduli, Acta Arith. 59 (1991), 59-70. MR 1133237 (92i:11014)
  • [6] S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. MR 0093493 (20:17)
  • [7] S. Znám, A survey of covering systems of congruences, Acta Math. Univ. Comenian. 40-41 (1982), 59-79. MR 686961 (84e:10004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11B25

Retrieve articles in all journals with MSC: 11B25

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society