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Covering the positive integers by disjoint sets of the form \(\{[n\alpha+\beta]: n=1,2,\dots \}\). (English) Zbl 0279.10042


MSC:

11B99 Sequences and sets
11A07 Congruences; primitive roots; residue systems
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References:

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[8] Skolem, Th, Über einige eigenshaften der zahlenmengen [αn + β] bei irrationalem α mit einleitenden bermerkungen über einige kombinatorische probleme, Norske vid. selsk. forh. (Trondheim), 30, 118-125, (1957)
[9] Skolem, Th, On certain distributions of integers in pairs with given differences, Math. scand., 5, 57-68, (1957) · Zbl 0084.04304
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[11] Uspensky, J.V, On a problem arising out of the theory of a certain game, Amer. math. monthly, 34, 516-526, (1927) · JFM 53.0167.05
[12] Znám, Ŝ, On exactly covering systems of arithmetic sequences, Math. ann., 180, 227-232, (1969) · Zbl 0169.37405
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