On Non-intersecting Arithmetic Progressions
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arithmeticnon-intersectingprogressionscommondifferenceserdosimprovesintegers
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We prove that if one has k non-intersecting arithmetic progressions of integers, with common differences 2 <= q_1,...,q_k <= x, then k < x exp((-1/6 + o(1)) sqrt(log x loglog x)). This improves a result of Szemeredi and Erdos.
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