Does there exist a constant $C>1$ such that, for every $n\ge 2$, there exists a sequence $z_i\in \mathbb{C}$ with $z_1=1$ and $|z_i|\ge 1$ for all $1\le i\le n$ with$$\underset{2\le k\le n+1}{\max }\left|\sum _{1\le i\le n}{z}_i^k\right|<C^{-n}?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

I don’t know of a definitive yes/no answer to **this exact formulation** [[nomath]](with the **shifted window** $k=2,\dots,n+1$, the **fixed term** $z_1=1$, and the **outside-the-unit-disk** constraint $|z_i|\ge 1$)[[/nomath]]. It sits right in the family of classical “pure power sum” problems of Turán/Chowla/Erdős–Atk…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.