Problem 196

Erdős Problem #196: declared status 'open'. Formalized: yes. Must every permutation of $\mathbb{N}$ contain a monotone 4-term arithmetic progression? In other words, given a permutation $x$ of $\mathbb{N}$ must there be indices with either $i<j<k<l$ or $i>j>k>l$ such that $x_i,x_j,x_k,x_l$ are an arithmetic progression? Prize: no. Tags: arithmetic progressions.