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Erdős problem 1186

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What is the minimum asymptotic density δk\delta_k of monochromatic kk-term arithmetic progressions in every two-colouring of {1,…,n}\{1, \dots, n\}? The exact certificate gives δ3=117/2192\delta_3 = 117/2192, matching the known 548-bead colouring.

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Additive Combinatorics102Arithmetic Progressions27
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