Erdős Problem #288

A claim by Ritvik Nayak with GPT-5.5 Thinking (3 May 2026) that has not yet been verified: candidate partial result.

Problem
Erdős problem #288 (number theory, unit fractions); current status: open
Credit
Ritvik Nayak with GPT-5.5 Thinking · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-05-03 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
UN-
VERIFIEDPer Tao's AI-contributions wiki

The problem

Is it true that there are only finitely many pairs of intervals I1,I2I_1,I_2 such that

∑n1∈I11n1+∑n2∈I21n2∈N?\sum_{n_1\in I_1}\frac{1}{n_1}+\sum_{n_2\in I_2}\frac{1}{n_2}\in \mathbb{N}?

Statement quoted from erdosproblems.com/288, maintained by Thomas Bloom. Original source: [ErGr80]. Current status there: open.

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
3 May, 2026 AI working with humans GPT-5.5 Thinking Ritvik Nayak ⚪ Candidate partial result

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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