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On odd covering systems with distinct moduli | | Song Guo
; Zhi-Wei Sun
; | | Date: |
10 Dec 2004 | | Journal: | Adv. Appl. Math. 35(2005), 182--187 | | Subject: | Number Theory; Combinatorics MSC-class: 11B25; 11A07; 11B75 | math.NT math.CO | | 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. | | Source: | arXiv, math.NT/0412217 | | Services: | Forum | Review | PDF | Favorites | |
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