Erdős problem 1186

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

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

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