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Does there exist a constant such that, for all large and all polynomials of degree with coefficients ,
Source: erdosproblems.com/1150
An accepted solution exists. The statement is false.
OPEN: the site's label (page last edited 23 January 2026; problem
page accessed 2026-10-06, its proof-claims tab empty). The derived standing
departs from the label, which predates the release: it is solved and disproved,
because Theorem 1.1 of the OpenAI release's manuscript of 23 September 2026
gives, for every and every large , signs whose polynomial of
length has maximum modulus at most on the circle, so no
works; this corpus's verification built its Lean declaration
OAI.AsymptoticallyMinimalLittlewood.main with only the three standard axioms
and audited its statement, and the corpus accepts it on
the claim page (OpenAI, 2026). No
acknowledgment outside this repository is known. The site's commentary, written
before the release, restates the question as whether ultraflat polynomials with
coefficients exist, notes that ultraflat polynomials do exist when the
coefficients may be any points of the unit circle
(Problem 230), so that the unimodular
analogue of the Statement has the answer no, notes that
is Parseval's identity, and points to the weaker
flatness question Problem 228. The
problem's discussion thread carries one earlier affirmative claim, el
Abdalaoui's preprint of 2025 that polynomials are never -flat
for even , to which the curator and Tao objected and which the
accepted theorem contradicts; it has the rejected claim page
el Abdalaoui 2025.
The same author claimed the affirmative answer earlier, in a 2016 preprint, and
again in September 2025; both claims have rejected claim pages
(2016,
September 2025).
Of the two release manuscripts of 5 October 2026, both without Lean, one claims
the two-sided ultraflat form
and the
other the lower bound with the same upper
bound; both are pending on Problem 228's claim page.