Necessary Conditions for Distinct Covering Systems with Square-free Moduli
Yin Jian-lian · Journal of Huaiyin Teachers College · 2004
Let A=｛a_s(m_s):s=1,…,k｝ be a finite system of arithmetic sequences that cover the integers where m_1,…,m_k and a_1,…,a_k∈Z. N is the least common multiple of the moduli.One fascinating problem on distinct covering systems (DCS) is if a DCS exist with all modulus odd In this paper we shall prove a necessary condition for A to be DCS consisting of odd square-free moduli.