Problem 973

Does there exist a constant $C>1$ such that, for every $n\geq 2$ , there exists a sequence $z_i\in \mathbb{C}$ with $z_1=1$ and $\lvert z_i\rvert \geq 1$ for all $1\leq i\leq n$ with

\max_{2\leq k\leq n+1}\left\lvert \sum_{1\leq i\leq n}z_i^k\right\rvert < C^{-n}?

Source: erdosproblems.com/973

Analysis

Wiki page

Status

ClaimedDisproved

A full solution has been claimed but not yet accepted. The statement is false.

Open. The site's proof-claims tab carries one full proof claim, filed 15 July 2026 by Luo, Yang and Zhu, who name GPT 5.6 Sol Pro on the tab, and the formal-conjectures statement file marks the problem research solved citing their preprint; the site's label is unchanged (OPEN; page last edited 23 January 2026, before the claim). The pending claims, both negative answers, are the page of Luo, Yang and Zhu and the page of Tan, Wang, Huang and Chen.

Problem 973

Status

Proof claims

Discussion