Erdős Problem #1151
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Statement
Let be the Lagrange interpolation polynomials of a continuous on the Chebyshev nodes. Prove that, for any closed , there exists a continuous function such that is the set of limit points of .
Context
An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open
A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.
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The solution was obtained with GPT-5.5 Pro using an explicit primitive-row decomposition of the Chebyshev-node measures; Theorem 1.1(a), the main contribution, was subsequently formalized largely autonomously by ChatGPT and Codex.
An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open
Reviews
0 human reviews · 1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Lean formalization of the result
Theorem 1.1(a), the main part of the contribution, is formalized in Lean and the formalization was confirmed correct on the forum; part (b) is unformalized because it depends on an Erdős result absent from mathlib. erdosproblems.com still lists the problem open.
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