A non-analytic proof of the newman—znám result for disjoint covering systems


A direct combinatorial proof is given to a generalization of the fact that the largest modulusN of a disjoint covering system appears at leastp times in the system, wherep is the smallest prime dividingN. The method is based on geometric properties of lattice parallelotopes.

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This research was supported by grant 85-00368 from the United States-Is rael Binational Science Foundation, Jerusalem, Israel.

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Berger, M.A., Felzenbaum, A. & Fraenkel, A.S. A non-analytic proof of the newman—znám result for disjoint covering systems. Combinatorica 6, 235–243 (1986). https://doi.org/10.1007/BF02579384

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