On Odd Covering Systems with Distinct

نویسندگان

  • SONG GUO
  • ZHI-WEI SUN
چکیده

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 greater than one. In this paper we show that if such a covering system {as(mod ns)}ks=1 exists with n1, . . . , nk all square-free, then the least common multiple of n1, . . . , nk has at least 22 prime divisors.

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On Odd Covering Systems with Distinct Moduli

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تاریخ انتشار 2004