Erdős problem 138 · problems.science

If $W(k)$ is the least $N$ such that every two-colouring of $\{1, \dots, N\}$ contains a monochromatic $k$ -term arithmetic progression, must $W(k+1) - W(k) \to \infty$ ?

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FormalConjectures/ErdosProblems/

138.lean

Retained formal statement6 of 9

Gowers [Go01] has proved $W(k) \leq 2^{2^{2^{2^{2^{k+9}}}}.$

FormalConjectures/ErdosProblems/138.leanErdos138.erdos_138.variants.upper1 lineExact file

1∀ (k : ℕ), Erdos138.W k ≤ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ (k + 9)

SolvedStatement only, no proof

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