Let $\mathbb{F}\_p$ be a finite field, $A=\{a\_1,\dots,a\_k\}\subset\mathbb{F}\_p^\*$ a $k$-element set, for $k<p$. $\mathfrak{S}\_k=$permutation gp.



> 
> **Question.** Is it true there is always a $\pi\in\mathfrak{S}\_k$ such that the following are pair-wise distinct in $\mathbb{F}\_p$?
>  $$a\_{\pi(1)}, \,a\_{\pi(1)}+a\_{\pi(2)},\,a\_{\pi(1)}+a\_{\pi(2)}+a\_{\pi(3)},\,\dots, \,a\_{\pi(1)}+\cdots+a\_{\pi(k)}.$$
> 
> 
> 


**EDIT.** Due to Julian Rosen's example, I change $A$ to be a subset of $\mathbb{F}\_p^\*$ (non-zero elements).



sum-sets in a finite field
It took me some effort to find the references you were requesting in your comment, but here they are eventually: 


* [Ordering subsets of the cyclic group to give distinct partial sums](https://mathoverflow.net/questions/164300/ordering-subsets-of-the-cyclic-group-to-give-distinct-partial-sums/203111#comment503832_203111) (posted to MO April 2014);
* [Geometry, Number Theory and Graph Theory of n-gon, permutation and graph labeling?](https://mathoverflow.net/questions/209408/geometry-number-theory-and-graph-theory-of-n-gon-permutation-and-graph-labelin/209496#209496) (posted to MO June 2015);
* ["On partial sums in cyclic groups"](https://arxiv.org/abs/1501.06872) by D. Archdeacon, J. Dinitz, A. Mattern, and D. Stinson, (*J. Combin. Math. Combin. Comput.* **98** (2016), 327–342).


As one can see, the problem is around for over 15 years at least.


