Erdős Problem #1038

Erdős problem #1038 · erdosproblems.com/1038

Among all nonconstant monic polynomials $f$ whose roots lie in $[-1, 1]$, determine $\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|$.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI co-developed

Method

Argument

Field

Extremal Polynomials

Posed by

—

Year posed

1958

Years open

68y

Solved

2026-07

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article