Erdős Problem #1133
OPENdatabase updated 2026-01-01
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \[\max_{x\in [-1,1]}\lvert P(x)\rvert >C.\] Yang [Ya26, Theorem 2.1] proved this, including repeated nodes, by taking \(\rho=0\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1133.Prizenone
Topicsanalysis, polynomials
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1133
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.