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15 August 2020
 
  » arxiv » math.NT/0409279

 Article overview


On the range of a covering function
Zhi-Wei Sun ;
Date 16 Sep 2004
Subject Number Theory; Combinatorics MSC-class: 11B25; 11A07; 11A25; 11B75; 11R04 | math.NT math.CO
AbstractLet {a_s(mod n_s)}_{s=1}^k (k>1) be a finite system of residue classes with the moduli n_1,...,n_k distinct. By means of algebraic integers we show that the range of the covering function w(x)=|{1le sle k: x=a_s (mod n_s)}| is not contained in any residue class with modulus greater one. In particular, the values of w(x) cannot have the same parity.
Source arXiv, math.NT/0409279
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