Erdős problem 138

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

Sources

The source's own material, retained exactly.

10 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

138.lean

Retained formal statement6 of 9

Gowers [Go01] has proved Unparsed notation: 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