Problem #197: Can $\mathbb{N}$ be partitioned into two sets, each of...

Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

SOLVED

Problem Statement

Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

Categories: Arithmetic Progressions

If three sets are allowed then this is possible.

Source: erdosproblems.com/197 | Last verified: January 14, 2026