Must every permutation of $N$ contain a monotone 4-term arithmetic progression? In other words, given a permutation $x$ of $N$ 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?

Worked, still open.

arithmetic progressions · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is a well-known open problem (asked by Erdős and Graham). It is listed as open as “Erdős Problem #196”. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 5 11 · open (literature)

theorem erdos_196 : answer(sorry) ↔ ∀ (f : ℕ ≃ ℕ), HasMonotoneAP f 4

open