On infinite disjoint covering systems
Authors:
Aviezri S. Fraenkel and R. Jamie Simpson
Journal:
Proc. Amer. Math. Soc. 119 (1993), 59
MSC:
Primary 11B25
MathSciNet review:
1148023
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Abstract: The structure of all infinite incongruent disjoint covering systems (IIDCS) whose moduli are divisible by no prime 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 , and the set of primes dividing the moduli is finite.
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 J. Beebee, Examples of infinite, incongruent exact covers, Amer. Math. Monthly 95 (1988), 121123. 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), 739742. MR 1130685 (92g:11009)
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 C. E. Krukenberg, Covering sets of the integers, Ph.D. Thesis, Univ. of Illinois, UrbanaChampaign, IL, 1971.
 [5]
 R. J. Simpson and D. Zeilberger, Necessary conditions for distinct covering systems with squarefree moduli, Acta Arith. 59 (1991), 5970. MR 1133237 (92i:11014)
 [6]
 S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289294. MR 0093493 (20:17)
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 S. Znám, A survey of covering systems of congruences, Acta Math. Univ. Comenian. 4041 (1982), 5979. MR 686961 (84e:10004)
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DOI:
http://dx.doi.org/10.1090/S00029939199311480238
PII:
S 00029939(1993)11480238
Article copyright:
© Copyright 1993
American Mathematical Society
