# 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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