Erdős Problem #888

Full solution by Przemek Chojecki with Aristotle and GPT-5.5 Pro (25 Apr 2026).

Problem
Erdős problem #888 (number theory, squares); current status: solved (Lean)
Credit
Przemek Chojecki with Aristotle and GPT-5.5 Pro · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-01-18 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
SOLVEDPer Tao's AI-contributions wiki

The problem

What is the size of the largest A⊆{1,…,n}A\subseteq \{1,\ldots,n\} such that if a≤b≤c≤d∈Aa\leq b\leq c\leq d\in A are such that abcdabcd is a square then ad=bcad=bc?

Statement quoted from erdosproblems.com/888, maintained by Thomas Bloom. Original source: [Er98,p.178]. Current status there: solved (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 Humans Outcome
18 Jan, 2026 AI on its own Claude Opus 4.5, Gemini 3 Pro, GPT-5.2 Thinking — 🔴 Incorrect proof found
25 Apr, 2026 AI working with humans Aristotle, GPT-5.5 Pro Przemek Chojecki 🟢 Full solution

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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