Necessary conditions for distinct covering systems with square-free moduli

  title={Necessary conditions for distinct covering systems with square-free moduli},
  author={R. Jamie Simpson and Doron Zeilberger},
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

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