On Odd Covering Systems with Distinct
نویسندگان
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.
منابع مشابه
On Odd Covering Systems with Distinct Moduli
A famous unsolved conjecture of P. Erdős and J. L. Selfridge states that there does not exist a covering system {as(mod ns)}s=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)}s=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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