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On the range of a covering function | Zhi-Wei Sun
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16 Sep 2004 | Subject: | Number Theory; Combinatorics MSC-class: 11B25; 11A07; 11A25; 11B75; 11R04 | math.NT math.CO | Abstract: | Let {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 | Services: | Forum | Review | PDF | Favorites |
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