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Problem 1038
Determine the infimum and supremum of
as ranges over all non-constant monic polynomials, all of whose roots are real and in the interval .
Source: erdosproblems.com/1038
- Analysis
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Claimed, AnsweredA full solution has been claimed but not yet accepted. Settled in another form, for example when its parts resolve differently or the question is open-ended.
Open. The site's proof-claims tab carries three full proof claims, each with AI systems named on the tab: by Shouqiao Wang (14 July 2026), by Tamás Darvas, Binghui Peng and Runzhou Tao (15 July 2026) and by Cristian Budala (24 August 2026); all three give the same infimum, and the site's label is unchanged (OPEN; page last edited 11 January 2026). The pending claims are Wang's page, the page of Darvas, Peng and Tao and Budala's page; the supremum alone is the accepted partial claim on Elbert's page and the pending partial claim on Tao's page.