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Erdos Problem #1061

Let $S(x)$ count ordered pairs $(a,b)$ with $a+b \le x$ and $\sigma(a)+\sigma(b) = \sigma(a+b)$. Erdos asked whether $S(x) \sim cx$. The opposite extreme holds: for every $R > 0$, $S(x)/(x(\log x)^R) \to \infty$, so the count beats every fixed logarithmic scale.

Exact FrontierDelta

Prior state unknowndisproved

Scope and record

Occurred: Jun 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Erdos Problem #1061 · Erdos 1061 · Problem 1061

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Eric Li
human · human collaborator

ChatGPT
model · ai model contributor · OpenAI / Harmonic

Aristotle
model · ai model contributor · OpenAI / Harmonic

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This event attributed to Eric Li

This event attributed to Aristotle

This event attributed to ChatGPT

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Erdos Problem #1061 — Mathematical Frontier Network