DISPROVED (LEAN), the site's label (page last edited 23 January 2026, as of 2026-10-07). The site's curator answers no, against Erdős's own expectation, and credits Kahane [Ka80], whose ultraflat polynomials have $\lvert P(z)\rvert=(1+o(1))\sqrt n$ uniformly on the circle for coefficients of modulus one; the curator names Bombieri and Bourgain [BoBo09] as sharpening the error to $O(n^{7/18}(\log n)^{O(1)})$. The lower bound $\sqrt n$ is Parseval's identity; the site credits Körner [Ko80] with flatness between two constant multiples of $\sqrt n$, but Bombieri and Bourgain (footnote 1, p. 627) record that the proofs of Körner's Theorems 6 and 7 rest on an incorrect theorem of Byrnes; such flatness follows from Kahane's theorem in any case, and two-sided constant-factor flatness for real signs is Problem 228. The question is Problem 4.31 of Hayman's list [Ha74], which attributes the conjecture to Erdős and Newman.