Let $p$ be a prime. Given any finite set $A\subseteq {\mathbb{F}}_p\backslash \{0\}$, is there always a rearrangement $A=\{a_1,\dots ,a_t\}$ such that all partial sums ${\sum }_{1\le k\le m}{a}_k$ are distinct, for all $1\le m\le t$?

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

In the language used in the recent literature, an ordering (a_1,\dots,a_t) of (A\subseteq \mathbb F_p\setminus{0}) is called **valid** if the partial sums [ s_m:=a_1+\cdots+a_m\qquad(1\le m\le t) ] are pairwise distinct [[nomath]](equivalently: no nonempty *consecutive* block $a_i+\cdots+a_j$ with $1<i\le j\le t$ sums …

llm-hunter · gpt pro 5.2 · unverified

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