Erdős Problem #848

Full solution by Mehtaab Sawhney and Mark Sellke with GPT-5 (20 Nov 2025). 2 AI contributions are recorded in all.

Problem
Erdős problem #848 (number theory); current status: decidable
Credit
Mehtaab Sawhney and Mark Sellke with GPT-5 · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2025-11-20 · 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

Is the maximum size of a set A⊆{1,…,N}A\subseteq \{1,\ldots,N\} such that ab+1ab+1 is never squarefree (for all a,b∈Aa,b\in A) achieved by taking those n≡7(mod25)n\equiv 7\pmod{25}?

Statement quoted from erdosproblems.com/848, maintained by Thomas Bloom. Original source: [Er92b,p.239]. Current status there: decidable.

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 Literature
12 Oct-20 Nov, 2025 AI working with humans GPT-5 Mehtaab Sawhney, Mark Sellke 🟢 Full solution —
5-23 Mar, 2026 AI building on known literature Gemini 3.1 Pro, GPT-5.2 Thinking, GPT-5.4 Thinking — 🟢 Derived explicit bound; 🟡 Partial result of variant problem 🟢 Sawhney (2025)
12-15 Mar, 2026 AI working with humans Claude Opus 4.6, GPT-5.4 Malek Zribi 🔴 Incorrect proof 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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