Exact covering systems in number fields (Q2922417)
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scientific article; zbMATH DE number 6353631
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exact covering systems in number fields |
scientific article; zbMATH DE number 6353631 |
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10 October 2014
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covering systems
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number fields
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0.9713409
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0.9100708
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0.90377903
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0.90116817
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0.89526296
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Exact covering systems in number fields (English)
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It has been conjectured by \textit{S. Kim} [Q. J. Math. 63, No. 1, 165--180 (2012; Zbl 1307.11111)] that in rings of integers of algebraic number fields there is no exact covering system of congruences having distinct moduli. He proved his conjecture for certain families of quadratic fields. The authors establish now this conjecture. The proof is based on the geometrical approach utilized by \textit{M. A. Berger} et al. [Combinatorica 6, 235--243 (1986; Zbl 0608.10006)] in the rational case.
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