On the Density of Integral Sets with Missing Differences
نویسندگان
چکیده
For a given set M of positive integers, a well-known problem of Motzkin asks for determining the maximal density μ(M) among sets of nonnegative integers in which no two elements differ by M . The problem is completely settled when |M | ≤ 2, and some partial results are known for several families of M for |M | ≥ 3. In this paper, we consider the case M = {a, b, c}, with c a multiple of a or b. In most cases, we obtain lower bounds for μ(M), which are conjecturally the exact values of μ(M), while in some we obtain the exact value of μ(M).
منابع مشابه
On the density of integral sets with missing differences from sets related to arithmetic progressions
Article history: Received 23 February 2010 Revised 12 August 2010 Accepted 18 September 2010 Available online xxxx Communicated by Matthias Beck
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