Erdős Problem #731

A claim by Eric Li with GPT (27 Jun 2026) that has not yet been verified: candidate full solution.

Problem
Erdős problem #731 (number theory, binomial coefficients); current status: open
Credit
Eric Li with GPT · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-06-27 · 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

Find some reasonable function f(n)f(n) such that, for almost all integers nn, the least integer mm such that m∤(2nn)m\nmid \binom{2n}{n} satisfies

m∼f(n).m\sim f(n).

Statement quoted from erdosproblems.com/731, maintained by Thomas Bloom. Original source: [EGRS75]. 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
27 Jun, 2026 AI working with humans GPT Eric Li ⚪ Candidate full solution

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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