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On odd covering systems with distinct moduli

Song Guo·Zhi-Wei Sun
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Abstract

A famous unsolved conjecture of P. Erdos and J. L. Selfridge states that there does not exist a covering system {a_s(mod n_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(mod n_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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Song Guo, Zhi-Wei Sun. 2005-09-14. On odd covering systems with distinct moduli. https://arxiv.org/abs/math/0412217

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