English

On odd covering systems with distinct moduli

Number Theory 2007-05-23 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.math/0412217,
  title  = {On odd covering systems with distinct moduli},
  author = {Song Guo and Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:math/0412217},
  year   = {2007}
}

Comments

7 pages, final version