Find the best function $f(d)$ such that, in any 2-colouring of the integers, at least one colour class contains an arithmetic progression with common difference $d$ of length $f(d)$ for infinitely many $d$.

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

This is a classical Erdős–Cohen problem (Erdős Problem #187), and **the exact “best” growth of $f(d)$ is not known**. What *is* known is a fairly sharp **upper bound** (via an explicit 2‑colouring construction) and only a very weak **lower bound** (that $f(d)$ must be unbounded).

llm-hunter · gpt pro 5.2 · unverified

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