Covering the Positive Integers
نویسنده
چکیده
For real numbers CL> 0 and /I, let S(or, fl) denote the set of integers {[WI + /I] : n = I, 2, 3,...} where, as usual, [x] denotes the greatest integer <.x. A finite family {S(q) pi) : 1 < i < r> of these sets is said to be an eventual covering fami& (ECF) if every sufficiently large integer occurs in exactly one S(CX~, pi). It is well known (e.g., see [I 11, [l], [6], [7]) that if all /3, are zero then the only ECF’s are:
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تاریخ انتشار 2003