Erdős problem 848 · problems.science

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 $n\equiv 7\pmod{25}$ ? Resolved for all sufficiently large $N$ : any near-maximal $A$ is contained in $\{n\equiv 7\pmod{25}\}$ or $\{n\equiv 18\pmod{25}\}$ , leaving only a finite check.

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AI collaborating with humans
Erdős AI contributions wiki · 12-15 Mar, 2026
Machine
Claude Opus 4.6, GPT-5.4
People
Malek Zribi
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AI building on literature
Erdős AI contributions wiki · 5-23 Mar, 2026
Machine
Gemini 3.1 Pro, GPT-5.2 Thinking, GPT-5.4 Thinking
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AI collaborating with humans
Erdős AI contributions wiki · 12 Oct-20 Nov, 2025
Machine
GPT-5
People
Mehtaab Sawhney, Mark Sellke
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Formalization
Erdős AI contributions wiki · 28 Jan, 2026
Machine
Aristotle, Claude, GPT-5.2
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argument
VibeMathed
Machine
GPT-5
People
Mehtaab Sawhney, Mark Sellke
Reported outcome
resolved
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