Problem 195

Erdős Problem #195: declared status 'open'. Formalized: yes. What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$-term arithmetic progression $x_1<\cdots<x_k$? Current best: Geneson [Ge19] proved that $k\leq 5$. Adenwalla [Ad22] proved that $k\leq 4$. Prize: no. Tags: arithmetic progressions.