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A connection between covers of Z and unit fractions | | Zhi-Wei Sun
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15 Nov 2004 | | Subject: | Number Theory; Combinatorics MSC-class: 11B25; 11B75; 11D68; 05A05 | math.NT math.CO | | Abstract: | Suppose that {a_s(mod n_s)}_{s=1}^k covers all the integers at least m times with the residue class a_k(mod n_k) irredundant. We show that if n_k is a period of the covering function w(x)=|{1le sle k: x=a_s (mod n_s)}| then for any r=0,1,...,n_k-1 there are at least m integers in the form sum_{s in I}1/n_s-r/n_k where I is a subset of {1,...,k-1}. | | Source: | arXiv, math.NT/0411305 | | Services: | Forum | Review | PDF | Favorites | |
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