Erdős Problem #645

GPT-5 found that the problem had already been solved in the literature (20 Oct 2025).

Problem
Erdős problem #645 (number theory, additive combinatorics, ramsey theory, arithmetic progressions); current status: proved (Lean)
Credit
GPT-5 · Literature search
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2025-10-20 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PRIOR
ARTPer Tao's AI-contributions wiki

The problem

If N\mathbb{N} is 2-coloured then must there exist a monochromatic three-term arithmetic progression x,x+d,x+2dx,x+d,x+2d such that d>xd>x?

Statement quoted from erdosproblems.com/645, maintained by Thomas Bloom. Original source: [Er80,p.93][Er95c]. Current status there: proved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Outcome
20 Oct, 2025 Literature search GPT-5 🟢 Full solution found

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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