Erdős Problem #396

Partial progress by Malek Zribi with Claude, Codex and GPT (15 Mar 2026): partial result. 2 AI contributions are recorded in all.

Problem
Erdős problem #396 (number theory, binomial coefficients); current status: open
Credit
Malek Zribi with Claude, Codex and GPT · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-03-15 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Is it true that for every kk there exists nn such that

∏0≤i≤k(n−i)∣(2nn)?\prod_{0\leq i\leq k}(n-i) \mid \binom{2n}{n}?

Statement quoted from erdosproblems.com/396, 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
15 Mar, 2026 AI working with humans Claude, Codex, GPT Malek Zribi 🟡 Partial result
5-7 Apr, 2026 AI working with humans GPT-5.4 Pro, GPT-5.4 Thinking Justin Dehorty, Nat Sothanaphan 🟡 Related 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.

∎