Abstract
In this paper it is shown that if every integer is covered bya 1+n 1ℤ,…,a k +n k ℤ exactlym times then for eachn=1,…,m there exist at least ( m n ) subsetsI of {1,…k} such that ∑ i ∈ I 1/n i equalsn. The bound ( m n ) is best possible.
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Research supported by the National Nature Science Foundation of P.R. of China.
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Sun, ZW. On exactlym times covers. Israel J. Math. 77, 345–348 (1992). https://doi.org/10.1007/BF02773696
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DOI: https://doi.org/10.1007/BF02773696