On the range of a covering function
Zhi-Wei Sun
Abstract
Let as(mod ns)s=1k (k>1) be a finite system of residue classes with the moduli n1,...,nk distinct. By means of algebraic integers we show that the range of the covering function w(x)=|1 s k: x=as (mod ns)| 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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