Result: On the range of a covering function

Title:
On the range of a covering function
Authors:
Zhi-Wei Sun
Source:
Journal of Number Theory. 111:190-196
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
arithmetic progression, 11B75, Algebra and Number Theory, covering function, Mathematics - Number Theory, Arithmetic progressions, Arithmetic functions, related numbers, inversion formulas, 11A07, 11B25, 11A25, 01 natural sciences, Covering function, covering system, Erdős–Selfridge conjecture, 11R04, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Congruences, primitive roots, residue systems, Number Theory (math.NT), Combinatorics (math.CO), 0101 mathematics, Cover of Z, Algebraic numbers, rings of algebraic integers
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
0022-314X
DOI:
10.1016/j.jnt.2004.11.004
DOI:
10.48550/arxiv.math/0409279
Access URL:
http://arxiv.org/abs/math/0409279
https://math.nju.edu.cn/~zwsun/69r.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0022314X04002586
https://core.ac.uk/display/21938702
https://www.sciencedirect.com/science/article/pii/S0022314X04002586#!
https://www.sciencedirect.com/science/article/pii/S0022314X04002586
http://math.nju.edu.cn/~zwsun/69r.pdf
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....5f2f4e334c288ed8bc3762d0d58ea4c9
Database:
OpenAIRE

Further Information

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)=|{1\le s\le 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.
7 pages; to appear in J. Number Theory