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22 September 2020
 
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On m-covers and m-systems
Zhi-Wei Sun ;
Date 16 Mar 2004
Subject Number Theory; Combinatorics MSC-class: 11B25; 05A05; 11A07; 11B75; 11D68 | math.NT math.CO
AbstractLet A={a_s(mod n_s)}_{s=0}^k be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results concerning system A. In particular, we show that if every integer lies in more than m=[sum_{s=1}^k 1/n_s] members of A, then for any a=0,1,2,... there are at least binom{m}{[a/n_0]} subsets I of {1,...,k} with sum_{s in I}1/n_s=a/n_0. We also characterize when any integer lies in at most m members of A, where m is a fixed positive integer.
Source arXiv, math.NT/0403271
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