Problem 160

Erdős Problem #160: declared status 'open'. Formalized: yes. Let $h(N)$ be the smallest $k$ such that $\{1,\ldots,N\}$ can be coloured with $k$ colours so that every four-term arithmetic progression must contain at least three distinct colours. Estimate $h(N)$. Prize: no. Tags: additive combinatorics, arithmetic progressions.