Erdős problem 966

Let $k,r\geq 2$ . Does there exist a set $A\subseteq \mathbb{N}$ that contains no non-trivial arithmetic progression of length $k+1$ , yet in any $r$ -colouring of $A$ there must exist a monochromatic non-trivial arithmetic progression of length $k$ ? Answered in the affirmative.

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

Retained excerpts/

VibeMathed

Retained source excerpt1 of 1

Let $k,r\geq 2$. Does there exist a set $A\subseteq \mathbb{N}$ that contains no non-trivial arithmetic progression of length $k+1$, yet in any $r$-colouring of $A$ there must exist a monochromatic non-trivial arithmetic progression of length $k$? Answered in the affirmative.

Open exact source location