Behaviour of the least root modulo a prime of a polynomial

Abstract

For a polynomial $f(x)\in \mathbb{Z}[x]$ without non-trivial linear relations among roots, we propose a conjecture on the distribution of the least root $r_p$ ($r_p\in \mathbb{Z},0\le r_p<p)$ of $f(x)\equiv 0\mathrm{mod}p$ where $p$ runs over the set of primes such that $f(x)$ modulo $p$ is fully splitting.

5 pages