On the range of a covering function

Details On the range of a covering function On the range of a covering function

2004-09-16

arxiv.org/abs/math/0409279v2

Mathematics

Number Theory

7 pages; to appear in J. Number Theory

Scientific paper

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.

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