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 $W(k+1) - W(k) \to \infty$ ?

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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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