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Unrolling Residues to Avoid Progressions

Steve Butler, Ron Graham and Linyuan Lu
Mathematics Magazine
Vol. 87, No. 2 (April 2014), pp. 83-94
DOI: 10.4169/math.mag.87.2.83
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.2.83
Page Count: 12
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Unrolling Residues to Avoid Progressions
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Abstract

Summary We look at the problem of coloring 1, 2, …, n with r colors to minimize the portion of monochromatic k-term arithmetic progressions. By using residues to color Zm and then unrolling, we produce the best-known colorings for several small values of r and k.

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