Erdős problem 188 · problems.science

What is the smallest $k$ such that $\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$ -term arithmetic progression of blue points with distance 1?

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FormalConjectures/ErdosProblems/

188.lean

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Old and new problems and results in combinatorial number theory by Erdős & Graham (Page 15):

How small can $M$ be made? The only estimate currently known is that $M \le 10000000$ (more or less). In the other direction, it has just been shown by R. Juhász [Ju (79)] that we must have $M \ge 5$ .

FormalConjectures/ErdosProblems/188.leanErdos188.erdos_188.variants.estimate1 lineExact file

1(∀ k ∈ Erdos188.s, 5 ≤ k) ∧ ∃ k ∈ Erdos188.s, k ≤ 10000000

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