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Discrepancy in arithmetic progressions
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DOI：10.1090/S0894-0347-96-00175-0.png)
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Abstract
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It is proven that there is a two-coloring of the first n integers for which all arithmetic progressions have discrepancy less than const.n(1/4). This shows that a 1964 result of K. F. Roth is, up to constants, best possible.
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