Erdős Problem #848

The problem

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

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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