Erdős Problem #986

The problem

For any fixed $s\geq 3$,

$$R(s,k) \gg \frac{k^{s-1}}{(\log k)^c}$$

for some constant $c=c(s)>0$.

Statement quoted from erdosproblems.com/986, maintained by Thomas Bloom. Original source: [Er90b,p.18]. Current status there: proved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

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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