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 statement4 of 9

When $p$ is prime Berlekamp [Be68] has proved $W(p+1) ≥ p^{2^p}$ .

FormalConjectures/ErdosProblems/138.leanErdos138.erdos_138.variants.prime1 lineExact file

1∀ (p : ℕ), Nat.Prime p → p * 2 ^ p ≤ Erdos138.W (p + 1)

SolvedStatement only, no proof