Erdős Problem #1133

The problem

Let $C>0$. There exists $\epsilon>0$ such that if $n$ is sufficiently large the following holds.

For any $x_1,\ldots,x_n\in [-1,1]$ there exist $y_1,\ldots,y_n\in [-1,1]$ such that, if $P$ is a polynomial of degree $m<(1+\epsilon)n$ with $P(x_i)=y_i$ for at least $(1-\epsilon)n$ many $1\leq i\leq n$, then

$$\max_{x\in [-1,1]}\lvert P(x)\rvert >C.$$

Statement quoted from erdosproblems.com/1133, maintained by Thomas Bloom. Original source: [Er67,p.72]. 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.

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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