On the Range of a Covering Function
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چکیده
Let {as(mod ns)}s=1 (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 6 s 6 k : x ≡ as (mod ns)}| is not contained in any residue class with modulus greater than one. In particular, the values of w(x) cannot have the same parity.
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تاریخ انتشار 2005