What is the largest $k$ such that in any permutation of $Z$ there must exist a monotone $k$ -term arithmetic progression $x_{1} < \dots < x_{k}$ ?

Worked, still open.

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

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

This is **not known** in full generality.

llm-hunter · gpt pro 5.2 · unverified

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

AMS 5 · open (literature)

theorem erdos_195 :
    answer(sorry) = sSup {k : ℕ | ∀ f : ℤ ≃ ℤ, HasMonotoneAP f k}

open