  Let $f(x)=x^n+a_{n-1}x^{n-1}+\dots+a_0$ be an irreducible polynomial with
integer coefficients. For a prime $p$ for which $f(x)$ is fully splitting
modulo $ p$, we consider $n$ roots $r_i$ of $f(x)\equiv 0\bmod p$ with $0 \le
r_1\le\dots\le r_n<p$ and propose several conjectures on the distribution of an
integer $\lceil \sum_{i\in S} r_i/p\rceil$ for a subset $S$ of $\{1,\dots,n\}$
when $p\to\infty$.
