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 statement8 of 9

FormalConjectures/ErdosProblems/138.leanErdos138.monoAPNumber_two_one1 lineExact file

1Erdos138.W 1 = 1

TestProof has a holeformal conjecturesexternal proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.