On odd covering systems with distinct moduli

@article{Guo2005OnOC,
  title={On odd covering systems with distinct moduli},
  author={Song-Tao Guo and Zhi-Wei Sun},
  journal={Adv. Appl. Math.},
  year={2005},
  volume={35},
  pages={182-187}
}
A famous unsolved conjecture of P. Erdos and J.L. Selfridge states that there does not exist a covering system {a"s(modn"s)}"s"="1^k with the moduli n"1,...,n"k odd, distinct and greater than one. In this paper we show that if such a covering system {a"s(modn"s)}"s"="1^k exists with n"1,...,n"k all square-free, then the least common multiple of n"1,...,n"k has at least 22 prime divisors. 
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Abstract. A famous unsolved conjecture of P. Erdős and J. L. Selfridge states that there does not exist a covering system {as(mod ns)}ks=1 with the moduli n1, . . . , nk odd, distinct and greaterExpand
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