Erdős Problem #138

Erdős problem #138 · erdosproblems.com/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 $W(k+1) - W(k) \to \infty$?

Result

Proved(see note)

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Ramsey Theory

Posed by

—

Year posed

1981

Years open

45y

Solved

2026-05-21

Model

AlphaProof Nexus

Vendor

Google DeepMind

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article